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Articoli di riviste sul tema "Singular stochastic partial differential equations"

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Autore: Grafiati

Pubblicato: 27 luglio 2024

Ultima modifica: 28 luglio 2024

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1

Matoussi, A., L. Piozin e A. Popier. "Stochastic partial differential equations with singular terminal condition". Stochastic Processes and their Applications 127, n. 3 (marzo 2017): 831–76. http://dx.doi.org/10.1016/j.spa.2016.07.002.

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2

Corwin, Ivan, e Hao Shen. "Some recent progress in singular stochastic partial differential equations". Bulletin of the American Mathematical Society 57, n. 3 (26 settembre 2019): 409–54. http://dx.doi.org/10.1090/bull/1670.

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3

Holm, Darryl D., e Tomasz M. Tyranowski. "Variational principles for stochastic soliton dynamics". Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 472, n. 2187 (marzo 2016): 20150827. http://dx.doi.org/10.1098/rspa.2015.0827.

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We develop a variational method of deriving stochastic partial differential equations whose solutions follow the flow of a stochastic vector field. As an example in one spatial dimension, we numerically simulate singular solutions (peakons) of the stochastically perturbed Camassa–Holm (CH) equation derived using this method. These numerical simulations show that peakon soliton solutions of the stochastically perturbed CH equation persist and provide an interesting laboratory for investigating the sensitivity and accuracy of adding stochasticity to finite dimensional solutions of stochastic partial differential equations. In particular, some choices of stochastic perturbations of the peakon dynamics by Wiener noise (canonical Hamiltonian stochastic deformations, CH-SD) allow peakons to interpenetrate and exchange order on the real line in overtaking collisions, although this behaviour does not occur for other choices of stochastic perturbations which preserve the Euler–Poincaré structure of the CH equation (parametric stochastic deformations, P-SD), and it also does not occur for peakon solutions of the unperturbed deterministic CH equation. The discussion raises issues about the science of stochastic deformations of finite-dimensional approximations of evolutionary partial differential equation and the sensitivity of the resulting solutions to the choices made in stochastic modelling.

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4

Ciotir, Ioana, e Jonas M. Tölle. "Nonlinear stochastic partial differential equations with singular diffusivity and gradient Stratonovich noise". Journal of Functional Analysis 271, n. 7 (ottobre 2016): 1764–92. http://dx.doi.org/10.1016/j.jfa.2016.05.013.

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5

Alhojilan, Yazid, Hamdy M. Ahmed e Wafaa B. Rabie. "Stochastic Solitons in Birefringent Fibers for Biswas–Arshed Equation with Multiplicative White Noise via Itô Calculus by Modified Extended Mapping Method". Symmetry 15, n. 1 (10 gennaio 2023): 207. http://dx.doi.org/10.3390/sym15010207.

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Stochastic partial differential equations have wide applications in various fields of science and engineering. This paper addresses the optical stochastic solitons and other exact stochastic solutions through birefringent fibers for the Biswas–Arshed equation with multiplicative white noise using the modified extended mapping method. This model contains many kinds of soliton solutions, which are always symmetric or anti-symmetric in space. Stochastic bright soliton solutions, stochastic dark soliton solutions, stochastic combo bright–dark soliton solutions, stochastic combo singular-bright soliton solutions, stochastic singular soliton solutions, stochastic periodic solutions, stochastic rational solutions, stochastic Weierstrass elliptic doubly periodic solutions, and stochastic Jacobi elliptic function solutions are extracted. The constraints on the parameters are considered to guarantee the existence of these stochastic solutions. Furthermore, some of the selected solutions are described graphically to demonstrate the physical nature of the obtained solutions.

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6

Eddahbi, Mhamed, Omar Kebiri e Abou Sene. "Infinite Horizon Irregular Quadratic BSDE and Applications to Quadratic PDE and Epidemic Models with Singular Coefficients". Axioms 12, n. 12 (21 novembre 2023): 1068. http://dx.doi.org/10.3390/axioms12121068.

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In an infinite time horizon, we focused on examining the well-posedness of problems for a particular category of Backward Stochastic Differential Equations having quadratic growth (QBSDEs) with terminal conditions that are merely square integrable and generators that are measurable. Our approach employs a Zvonkin-type transformation in conjunction with the Itô–Krylov’s formula. We applied our findings to derive probabilistic representation of a particular set of Partial Differential Equations par have quadratic growth in the gradient (QPDEs) characterized by coefficients that are measurable and almost surely continuous. Additionally, we explored a stochastic control optimization problem related to an epidemic model, interpreting it as an infinite time horizon QBSDE with a measurable and integrable drifts.

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7

Yang, Juan, Jianliang Zhai e Qing Zhou. "The Small Time Asymptotics of SPDEs with Reflection". Abstract and Applied Analysis 2014 (2014): 1–13. http://dx.doi.org/10.1155/2014/264263.

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We study stochastic partial differential equations with singular drifts and with reflection, driven by space-time white noise with nonconstant diffusion coefficients under periodic boundary conditions. The existence and uniqueness of invariant measures is established under appropriate conditions. As a byproduct, the Hölder continuity of the solution is obtained. The strong Feller property is also obtained. Moreover, we show large deviation principle.

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8

Al-Sawalha, M. Mossa, Humaira Yasmin, Rasool Shah, Abdul Hamid Ganie e Khaled Moaddy. "Unraveling the Dynamics of Singular Stochastic Solitons in Stochastic Fractional Kuramoto–Sivashinsky Equation". Fractal and Fractional 7, n. 10 (12 ottobre 2023): 753. http://dx.doi.org/10.3390/fractalfract7100753.

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This work investigates the complex dynamics of the stochastic fractional Kuramoto–Sivashinsky equation (SFKSE) with conformable fractional derivatives. The research begins with the creation of singular stochastic soliton solutions utilizing the modified extended direct algebraic method (mEDAM). Comprehensive contour, 3D, and 2D visual representations clearly depict the categorization of these stochastic soliton solutions as kink waves or shock waves, offering a clear description of these soliton behaviors within the context of the SFKSE framework. The paper also illustrates the flexibility of the transformation-based approach mEDAM for investigating soliton occurrence not only in SFKSE but also in a wide range of nonlinear fractional partial differential equations (FPDEs). Furthermore, the analysis considers the effect of noise, specifically Brownian motion, on soliton solutions and wave dynamics, revealing the significant influence of randomness on the propagation, generation, and stability of soliton in complex stochastic systems and advancing our understanding of extreme behaviors in scientific and engineering domains.

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9

Shen, Hao. "A stochastic PDE approach to large N problems in quantum field theory: A survey". Journal of Mathematical Physics 63, n. 8 (1 agosto 2022): 081103. http://dx.doi.org/10.1063/5.0089851.

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In this Review, we review some recent rigorous results on large N problems in quantum field theory, stochastic quantization, and singular stochastic partial differential equations (SPDEs) and their mean field limit problems. In particular, we discuss the O( N) linear sigma model on a two- and three-dimensional torus. The stochastic quantization procedure leads to a coupled system of N interacting Φ4 equations. In d = 2, we show uniformity in N bounds for the dynamics and convergence to a mean-field singular SPDE. For large enough mass or small enough coupling, the invariant measures [i.e., the O( N) linear sigma model] converge to the massive Gaussian free field, the unique invariant measure of the mean-field dynamics, in a Wasserstein distance. We also obtain tightness for certain O( N) invariant observables as random fields in suitable Besov spaces as N → ∞, along with exact descriptions of the limiting correlations. In d = 3, the estimates become more involved since the equation is more singular. We discuss in this case how to prove convergence to the massive Gaussian free field. The proofs of these results build on the recent progress of singular SPDE theory and combine many new techniques, such as uniformity in N estimates and dynamical mean field theory. These are based on joint papers with Scott Smith, Rongchan Zhu, and Xiangchan Zhu.

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10

Ur Rehman, Hamood, Aziz Ullah Awan, Sayed M. Eldin e Ifrah Iqbal. "Study of optical stochastic solitons of Biswas-Arshed equation with multiplicative noise". AIMS Mathematics 8, n. 9 (2023): 21606–21. http://dx.doi.org/10.3934/math.20231101.

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<abstract><p>In many nonlinear partial differential equations, noise or random fluctuation is an inherent part of the system being modeled and have vast applications in different areas of engineering and sciences. This objective of this paper is to construct stochastic solitons of Biswas-Arshed equation (BAE) under the influence of multiplicative white noise in the terms of the Itô calculus. Bright, singular, dark, periodic, singular and combined singular-dark stochastic solitons are attained by using the Sardar subequation method. The results prove that the suggested approach is a very straightforward, concise and dynamic addition in literature. By using Mathematica 11, some 3D and 2D plots are illustrated to check the influence of multiplicative noise on solutions. The presence of multiplicative noise leads the fluctuations and have significant effects on the long-term behavior of the system. So, it is observed that multiplicative noise stabilizes the solutions of BAE around zero.</p></abstract>

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11

Ahmed, Muhammad Ozair, Rishi Naeem, Muhammad Akhtar Tarar, Muhammad Sajid Iqbal, Mustafa Inc e Farkhanda Afzal. "Existence theories and exact solutions of nonlinear PDEs dominated by singularities and time noise". Nonlinear Analysis: Modelling and Control 28 (9 gennaio 2023): 1–15. http://dx.doi.org/10.15388/namc.2023.28.30563.

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The current research deals with the exact solutions of the nonlinear partial differential equations having two important difficulties, that is, the coefficient singularities and the stochastic function (white noise). There are four major contributions to contemporary research. One is the mathematical analysis where the explicit a priori estimates for the existence of solutions are constructed by Schauder’s fixed point theorem. Secondly, the control of the solution behavior subject to the singular parameter ϵ when ϵ → 0. Thirdly, the impact of noise that is present in the differential equation has been successfully handled in exact solutions. The final contribution is to simulate the exact solutions and explain the plots.

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12

Linares, Pablo, Felix Otto e Markus Tempelmayr. "The structure group for quasi-linear equations via universal enveloping algebras". Communications of the American Mathematical Society 3, n. 1 (20 gennaio 2023): 1–64. http://dx.doi.org/10.1090/cams/16.

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We replace trees by multi-indices as an index set of the abstract model space to tackle quasi-linear singular stochastic partial differential equations. We show that this approach is consistent with the postulates of regularity structures when it comes to the structure group, which arises from a Hopf algebra and a comodule. Our approach, where the dual of the abstract model space naturally embeds into a formal power series algebra, allows to interpret the structure group as a Lie group arising from a Lie algebra consisting of derivations on this power series algebra. These derivations in turn are the infinitesimal generators of two actions on the space of pairs (non-linearities, functions of space-time mod constants). We also argue that there exist pre-Lie algebra and Hopf algebra morphisms between our structure and the tree-based one in the cases of branched rough paths (Grossman-Larson, Connes-Kreimer) and of the stochastic heat equation.

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13

Seçgin, Abdullah, e Murat Kara. "Vibration bounding of uncertain thin beams by using an extreme value model based on statistical moments". Journal of Vibration and Control 24, n. 23 (15 marzo 2018): 5627–41. http://dx.doi.org/10.1177/1077546318763203.

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The paper introduces an extreme value model based on statistical moments to predict modal and vibration response bounds for stochastic structures. The approach is applied to a thin beam having two input uncertain parameters: elasticity modulus and specific volume (inverse of the mass density). The input parameters are controllably generated with random shifted normal distributions that have positive statistics. Then the first two statistical moments, mean and standard deviation of natural frequency, and bending vibration displacement are predicted by solving stochastic differential equation of bending vibration of thin beams. Here, the differential equation is solved by utilizing a powerful numerical technique, discrete singular convolution. The accuracies of the discrete singular convolution method and the statistical moment approach are separately ensured with analytical comparisons and experimental and numerical Monte Carlo simulations. These statistical moments are then processed by an extreme value model to predict uncertainty bounds for modal and vibration displacement responses. Predicted bounds are compared with random responses obtained by numerical Monte Carlo simulations. The proposed approach estimates very accurate results with less computation memory and time compared to Monte Carlo solutions. Therefore, the approach proves its efficiency in the use of uncertainty propagation problems governed by partial differential equations.

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14

Morzfeld, M., e A. J. Chorin. "Implicit particle filtering for models with partial noise, and an application to geomagnetic data assimilation". Nonlinear Processes in Geophysics 19, n. 3 (19 giugno 2012): 365–82. http://dx.doi.org/10.5194/npg-19-365-2012.

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Abstract. Implicit particle filtering is a sequential Monte Carlo method for data assimilation, designed to keep the number of particles manageable by focussing attention on regions of large probability. These regions are found by minimizing, for each particle, a scalar function F of the state variables. Some previous implementations of the implicit filter rely on finding the Hessians of these functions. The calculation of the Hessians can be cumbersome if the state dimension is large or if the underlying physics are such that derivatives of F are difficult to calculate, as happens in many geophysical applications, in particular in models with partial noise, i.e. with a singular state covariance matrix. Examples of models with partial noise include models where uncertain dynamic equations are supplemented by conservation laws with zero uncertainty, or with higher order (in time) stochastic partial differential equations (PDE) or with PDEs driven by spatially smooth noise processes. We make the implicit particle filter applicable to such situations by combining gradient descent minimization with random maps and show that the filter is efficient, accurate and reliable because it operates in a subspace of the state space. As an example, we consider a system of nonlinear stochastic PDEs that is of importance in geomagnetic data assimilation.

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15

Hafayed, Mokhtar, Abdelmadjid Abba e Syed Abbas. "On partial-information optimal singular control problem for mean-field stochastic differential equations driven by Teugels martingales measures". International Journal of Control 89, n. 2 (2 settembre 2015): 397–410. http://dx.doi.org/10.1080/00207179.2015.1079648.

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16

Kim, Ildoo, e Kyeong-Hun Kim. "On the $L_p$-boundedness of the stochastic singular integral operators and its application to $L_p$-regularity theory of stochastic partial differential equations". Transactions of the American Mathematical Society 373, n. 8 (26 maggio 2020): 5653–84. http://dx.doi.org/10.1090/tran/8089.

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17

Bonnet, Celine, Keltoum Chahour, Frédérique Clément, Marie Postel e Romain Yvinec. "Multiscale population dynamics in reproductive biology: singular perturbation reduction in deterministic and stochastic models". ESAIM: Proceedings and Surveys 67 (2020): 72–99. http://dx.doi.org/10.1051/proc/202067006.

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In this study, we describe different modeling approaches for ovarian follicle population dynamics, based on either ordinary (ODE), partial (PDE) or stochastic (SDE) differential equations, and accounting for interactions between follicles. We put a special focus on representing the population-level feedback exerted by growing ovarian follicles onto the activation of quiescent follicles. We take advantage of the timescale difference existing between the growth and activation processes to apply model reduction techniques in the framework of singular perturbations. We ﬁrst study the linear versions of the models to derive theoretical results on the convergence to the limit models. In the nonlinear cases, we provide detailed numerical evidence of convergence to the limit behavior. We reproduce the main semi-quantitative features characterizing the ovarian follicle pool, namely a bimodal distribution of the whole population, and a slope break in the decay of the quiescent pool with aging.

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18

SHARDIN, ANTON A., e MICHAELA SZÖLGYENYI. "OPTIMAL CONTROL OF AN ENERGY STORAGE FACILITY UNDER A CHANGING ECONOMIC ENVIRONMENT AND PARTIAL INFORMATION". International Journal of Theoretical and Applied Finance 19, n. 04 (25 maggio 2016): 1650026. http://dx.doi.org/10.1142/s0219024916500266.

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In this paper, we consider an energy storage optimization problem in finite time in a model with partial information that allows for a changing economic environment. The state process consists of the storage level controlled by the storage manager and the energy price process, which is a diffusion process the drift of which is assumed to be unobservable. We apply filtering theory to find an alternative state process which is adapted to our observation filtration. For this alternative state process, we derive the associated Hamilton–Jacobi–Bellman equation and solve the optimization problem numerically. This results in a candidate for the optimal policy for which it is a priori not clear whether the controlled state process exists. Hence, we prove an existence and uniqueness result for a class of time-inhomogeneous stochastic differential equations with discontinuous drift and singular diffusion coefficient. Finally, we apply our result to prove admissibility of the candidate optimal control.

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19

Cavenago, M. "A model of radiofrequency and plasma coupling for compact ion sources and design". Journal of Instrumentation 19, n. 01 (1 gennaio 2024): C01017. http://dx.doi.org/10.1088/1748-0221/19/01/c01017.

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Abstract Inductive coupling of radiofrequency power to plasma is a complicate process, since it depends from the density of plasma itself, because ionization is a chain reaction process, and, at low density a capacitive coupling may mix with inductive coupling (with no Faraday screen). Plasma temperature Te , density ne and vector potential are closely coupled, giving nonlinear and singular systems of Partial Differential equations, which require slow iterative solutions, motivating the consideration of a 2D model, also as rapid design and first approximation tool. Plasma conductivity and heating depend on collision rate, which includes also the so-called stochastic collisions (mainly electron collisions with walls), proportionally more important at low gas density ng . Conductivity is also affected by static and radiofrequency magnetic fields; results for skin depth and stochastic collision estimates are reported. The transport of Te and ne inside source can be controlled by a magnetic filter B f . Considering a 5 cm radius H- ion source as example, solution of ne and Te are reported as a function of filter strength B fa, applied rf power and wall status; solver convergence methods and key plasma observables are briefly discussed. Due to small dimension, a filter strength B fa in the order of 8 mT is needed to achieve electron temperature lower than 2 eV (for negative ion production) at extraction.

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20

Kontrec, Nataša, Jelena Vujaković, Marina Tošić, Stefan Panić e Biljana Panić. "Mathematical Modeling of Integral Characteristics of Repair Process under Maintenance Contracts". Symmetry 13, n. 12 (8 dicembre 2021): 2360. http://dx.doi.org/10.3390/sym13122360.

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The repair rate is a very important parameter for system maintainability and can be defined as a frequency of successfully performed repair actions on a failed component per unit of time. This paper analyzes the integral characteristics of a stochastic repair rate for corresponding values of availability in a system operating under maintenance contracts. The probability density function (PDF) of the repair rate has been studied extensively and it was concluded that it is not a symmetric function so its mean value does not correspond to its maximum. Based on that, the equation for the envelope line of the PDF maximums of the repair rate has been provided. Namely, instead of repair rate PDF equations, we can use envelope line parameters for certain calculations, which are expressed in a simpler mathematical form. That will reduce time required for calculations and prediction and enhance reactions in failure events. Further, for the analytical and numerical evaluation of a system performance, the annual repair rate PDFs are analyzed, such as particular solutions of corresponding differential equation, while the existence of a singular solution is considered and analyzed under different conditions. Moreover, we derived optimal values of availability for which the PDF maximums have been obtained. Finally, in order to generalize the behavior of the repair process, a partial differential equation, as a function of the repair rate process and availability parameter, has been formed.

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21

Lei, Ting, e Guanggan Chen. "Dominant dynamics for a class of singularly perturbed stochastic partial differential equations with quadratic nonlinearities and random Neumann boundary conditions". Chaos: An Interdisciplinary Journal of Nonlinear Science 31, n. 7 (luglio 2021): 073109. http://dx.doi.org/10.1063/5.0042117.

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22

Rutkowski, Marek. "Stochastic differential equations with singular drift". Statistics & Probability Letters 10, n. 3 (agosto 1990): 225–29. http://dx.doi.org/10.1016/0167-7152(90)90078-l.

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23

Kabanov, Yu M., e S. M. Pergamenshchikov. "SINGULAR PERTURBATIONS OF STOCHASTIC DIFFERENTIAL EQUATIONS". Mathematics of the USSR-Sbornik 71, n. 1 (28 febbraio 1992): 15–27. http://dx.doi.org/10.1070/sm1992v071n01abeh001274.

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24

Wang, Feng-Yu. "Singular density dependent stochastic differential equations". Journal of Differential Equations 361 (luglio 2023): 562–89. http://dx.doi.org/10.1016/j.jde.2023.03.038.

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25

BOUFOUSSI, B., e N. MRHARDY. "MULTIVALUED STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS VIA BACKWARD DOUBLY STOCHASTIC DIFFERENTIAL EQUATIONS". Stochastics and Dynamics 08, n. 02 (giugno 2008): 271–94. http://dx.doi.org/10.1142/s0219493708002317.

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In this paper, we establish by means of Yosida approximation, the existence and uniqueness of the solution of a backward doubly stochastic differential equation whose coefficient contains the subdifferential of a convex function. We will use this result to prove the existence of stochastic viscosity solution for some multivalued parabolic stochastic partial differential equation.

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26

Dzhuraev, A. "On some singular partial differential equations". Applicable Analysis 73, n. 1-2 (ottobre 1999): 65–76. http://dx.doi.org/10.1080/00036819908840763.

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27

Motamed, Mohammad. "Fuzzy-Stochastic Partial Differential Equations". SIAM/ASA Journal on Uncertainty Quantification 7, n. 3 (gennaio 2019): 1076–104. http://dx.doi.org/10.1137/17m1140017.

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Barles, Guy, Rainer Buckdahn e Etienne Pardoux. "Backward stochastic differential equations and integral-partial differential equations". Stochastics and Stochastic Reports 60, n. 1-2 (febbraio 1997): 57–83. http://dx.doi.org/10.1080/17442509708834099.

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29

Cherny, A. S. "Invariant Distributions for Singular Stochastic Differential Equations". Stochastics and Stochastic Reports 76, n. 2 (aprile 2004): 101–12. http://dx.doi.org/10.1080/10451120410001697837.

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30

Fleming, W. H., e M. Nisio. "Differential games for stochastic partial differential equations". Nagoya Mathematical Journal 131 (settembre 1993): 75–107. http://dx.doi.org/10.1017/s0027763000004554.

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In this paper we are concerned with zero-sum two-player finite horizon games for stochastic partial differential equations (SPDE in short). The main aim is to formulate the principle of dynamic programming for the upper (or lower) value function and investigate the relationship between upper (or lower) value function and viscocity solution of min-max (or max-min) equation on Hilbert space.

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Zhang, Qi, e Huaizhong Zhao. "Mass-conserving stochastic partial differential equations and backward doubly stochastic differential equations". Journal of Differential Equations 331 (settembre 2022): 1–49. http://dx.doi.org/10.1016/j.jde.2022.05.015.

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Zhu, QingFeng, e YuFeng Shi. "Forward-backward doubly stochastic differential equations and related stochastic partial differential equations". Science China Mathematics 55, n. 12 (20 maggio 2012): 2517–34. http://dx.doi.org/10.1007/s11425-012-4411-1.

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Pongérard, Patrice. "NONLINEAR SYSTEM OF SINGULAR PARTIAL DIFFERENTIAL EQUATIONS". Journal of Mathematical Sciences: Advances and Applications 43 (10 gennaio 2017): 31–53. http://dx.doi.org/10.18642/jmsaa_7100121748.

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Koike, Minoru. "Overdetermined systems of singular partial differential equations". Nonlinear Analysis: Theory, Methods & Applications 30, n. 6 (dicembre 1997): 3855–65. http://dx.doi.org/10.1016/s0362-546x(96)00235-0.

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Bruned, Yvain, Martin Hairer e Lorenzo Zambotti. "Renormalisation of Stochastic Partial Differential Equations". EMS Newsletter 2020-3, n. 115 (3 marzo 2020): 7–11. http://dx.doi.org/10.4171/news/115/3.

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Pratelli, M., R. Carmona e B. Rozovskii. "Stochastic Partial Differential Equations: Six Perspectives". Journal of the American Statistical Association 95, n. 450 (giugno 2000): 688. http://dx.doi.org/10.2307/2669432.

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Da Prato, G., e L. Tubaro. "Fully Nonlinear Stochastic Partial Differential Equations". SIAM Journal on Mathematical Analysis 27, n. 1 (gennaio 1996): 40–55. http://dx.doi.org/10.1137/s0036141093256769.

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38

Allen, Edward J. "Derivation of Stochastic Partial Differential Equations". Stochastic Analysis and Applications 26, n. 2 (7 marzo 2008): 357–78. http://dx.doi.org/10.1080/07362990701857319.

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Hofmanová, Martina. "Degenerate parabolic stochastic partial differential equations". Stochastic Processes and their Applications 123, n. 12 (dicembre 2013): 4294–336. http://dx.doi.org/10.1016/j.spa.2013.06.015.

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Chen, Zhen-Qing, Kyeong-Hun Kim e Panki Kim. "Fractional time stochastic partial differential equations". Stochastic Processes and their Applications 125, n. 4 (aprile 2015): 1470–99. http://dx.doi.org/10.1016/j.spa.2014.11.005.

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Lions, Pierre-Louis, e Panagiotis E. Souganidis. "Fully nonlinear stochastic partial differential equations". Comptes Rendus de l'Académie des Sciences - Series I - Mathematics 326, n. 9 (maggio 1998): 1085–92. http://dx.doi.org/10.1016/s0764-4442(98)80067-0.

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Di Nunno, Giulia, e Tusheng Zhang. "Approximations of stochastic partial differential equations". Annals of Applied Probability 26, n. 3 (giugno 2016): 1443–66. http://dx.doi.org/10.1214/15-aap1122.

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BRZEŹNIAK, Z., M. CAPIŃSKI e F. FLANDOLI. "STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS AND TURBULENCE". Mathematical Models and Methods in Applied Sciences 01, n. 01 (marzo 1991): 41–59. http://dx.doi.org/10.1142/s0218202591000046.

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Stochastic partial differential equations are proposed in order to model some turbulence phenomena. A particular case (the stochastic Burgers equations) is studied. Global existence of solutions is proved. Their regularity is also studied in detail. It is shown that the solutions cannot possess too high regularity.

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44

Ashyralyev, Allaberen, e Ülker Okur. "Stability of Stochastic Partial Differential Equations". Axioms 12, n. 7 (24 luglio 2023): 718. http://dx.doi.org/10.3390/axioms12070718.

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In this paper, we study the stability of the stochastic parabolic differential equation with dependent coefficients. We consider the stability of an abstract Cauchy problem for the solution of certain stochastic parabolic differential equations in a Hilbert space. For the solution of the initial-boundary value problems (IBVPs), we obtain the stability estimates for stochastic parabolic equations with dependent coefficients in specific applications.

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45

Buckdahn, Rainer, e Shige Peng. "Stationary backward stochastic differential equations and associated partial differential equations". Probability Theory and Related Fields 115, n. 3 (1999): 383. http://dx.doi.org/10.1007/s004400050242.

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46

Zhu, Jie. "The Mean Field Forward Backward Stochastic Differential Equations and Stochastic Partial Differential Equations". Pure and Applied Mathematics Journal 4, n. 3 (2015): 120. http://dx.doi.org/10.11648/j.pamj.20150403.20.

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47

BAKHTIN, YURI, e JONATHAN C. MATTINGLY. "STATIONARY SOLUTIONS OF STOCHASTIC DIFFERENTIAL EQUATIONS WITH MEMORY AND STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS". Communications in Contemporary Mathematics 07, n. 05 (ottobre 2005): 553–82. http://dx.doi.org/10.1142/s0219199705001878.

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We explore Itô stochastic differential equations where the drift term possibly depends on the infinite past. Assuming the existence of a Lyapunov function, we prove the existence of a stationary solution assuming only minimal continuity of the coefficients. Uniqueness of the stationary solution is proven if the dependence on the past decays sufficiently fast. The results of this paper are then applied to stochastically forced dissipative partial differential equations such as the stochastic Navier–Stokes equation and stochastic Ginsburg–Landau equation.

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48

Zhu, Qingfeng, e Yufeng Shi. "Backward doubly stochastic differential equations with jumps and stochastic partial differential-integral equations". Chinese Annals of Mathematics, Series B 33, n. 1 (gennaio 2012): 127–42. http://dx.doi.org/10.1007/s11401-011-0686-8.

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49

Shoimkulov, Boitura. "Integral representation of solution manifolds for over determined systems with one singular line". Вестник Пермского университета. Математика. Механика. Информатика, n. 2(53) (2021): 5–9. http://dx.doi.org/10.17072/1993-0550-2021-2-5-9.

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Abstract (sommario):

In this paper, an over determined system of second-order partial differential equations with one singular line is investigated. A compatibility condition is found for over determined systems of second-order partial differential equations with one singular line. Under the condition of compatibility, introducing a new function, we come to a over determined system of partial differential equations of the second order with one singular line of a simpler form. The integral representation of the manifold of solutions of the redefined second-order partial differential system with one singular line is found explicitly through three arbitrary constants, for which initial data problems (Cauchy type problems) can be posed.

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50

Shoimkulov, B. M. "Of one over determined system differential equation at private derivative second order with one singular point and one singular line". Вестник Пермского университета. Математика. Механика. Информатика, n. 4(55) (2021): 14–18. http://dx.doi.org/10.17072/1993-0550-2021-4-14-18.

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Abstract (sommario):

In this paper, a over determined system of second-order partial differential equations with one singular point and one singular line is investigated. A compatibility condition is found for over determined systems of second-order partial differential equations with one singular point and one singular line. If the compatibility condition is met, integral representations of the variety of solutions are found explicitly in terms of three arbitrary constants, when the singular line is in the boundaries of the domain for which initial data problems (Cauchy-type Problems) can be set. In this paper considers a redefined system of second-order partial differential equations, when the coefficients and right parts have one singular point and one singular line. Obtaining a variety of solutions and studying boundary value problems for linear differential equations of the hyperbolic type of the second order, some linear redefined systems of the first and second order with one and two supersingular lines and supersingular points is devoted to the monograph of academician of the National Academy of Sciences of the Republic of Tatarstan Rajabov N. - 1992 "Introduction to the theory of partial differential equations with supersingular coefficients" [6, p.126]. Using the obtained results of The monograph of Rajabov N., a variety of solutions of redefined systems of partial differential equations of the second order with one singular point and one singular line in an explicit form, through three arbitrary constants, was found.

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