Relevant bibliographies by topics / Partial differential equations

Academic literature on the topic 'Partial differential equations'

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Published: 4 June 2021
Last updated: 30 July 2024

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Journal articles on the topic "Partial differential equations"

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Tumajer, František. "Controllable systems of partial differential equations." Applications of Mathematics 31, no. 1 (1986): 41–53. http://dx.doi.org/10.21136/am.1986.104183.

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Tiwari, Chinta Mani, and Richa Yadav. "Distributional Solutions to Nonlinear Partial Differential Equations." International Journal of Research Publication and Reviews 5, no. 4 (April 11, 2024): 6441–47. http://dx.doi.org/10.55248/gengpi.5.0424.1085.

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Hibberd, S., Richard Bellman, and George Adomian. "Partial Differential Equations." Mathematical Gazette 71, no. 458 (December 1987): 341. http://dx.doi.org/10.2307/3617100.

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Abbott, Steve, and Lawrence C. Evans. "Partial Differential Equations." Mathematical Gazette 83, no. 496 (March 1999): 185. http://dx.doi.org/10.2307/3618751.

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Chang, Sun-Yung Alice, Camillo De Lellis, and Reiner Schätzle. "Partial Differential Equations." Oberwolfach Reports 10, no. 3 (2013): 2259–319. http://dx.doi.org/10.4171/owr/2013/40.

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Chang, Sun-Yung Alice, Camillo De Lellis, and Peter Topping. "Partial Differential Equations." Oberwolfach Reports 12, no. 3 (2015): 2065–124. http://dx.doi.org/10.4171/owr/2015/36.

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De Lellis, Camillo, Richard Schoen, and Peter Topping. "Partial Differential Equations." Oberwolfach Reports 14, no. 3 (July 4, 2018): 2165–222. http://dx.doi.org/10.4171/owr/2017/35.

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De Philippis, Guido, Richard Schoen, and Peter Topping. "Partial Differential Equations." Oberwolfach Reports 16, no. 3 (September 9, 2020): 2033–97. http://dx.doi.org/10.4171/owr/2019/34.

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Evans, W. D. "PARTIAL DIFFERENTIAL EQUATIONS." Bulletin of the London Mathematical Society 20, no. 4 (July 1988): 375–76. http://dx.doi.org/10.1112/blms/20.4.375.

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Satty, ThomasL. "Partial differential equations." Computers & Mathematics with Applications 11, no. 1-3 (January 1985): 1–4. http://dx.doi.org/10.1016/0898-1221(85)90135-x.

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Dissertations / Theses on the topic "Partial differential equations"

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Dareiotis, Anastasios Constantinos. "Stochastic partial differential and integro-differential equations." Thesis, University of Edinburgh, 2015. http://hdl.handle.net/1842/14186.

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In this work we present some new results concerning stochastic partial differential and integro-differential equations (SPDEs and SPIDEs) that appear in non-linear filtering. We prove existence and uniqueness of solutions of SPIDEs, we give a comparison principle and we suggest an approximation scheme for the non-local integral operators. Regarding SPDEs, we use techniques motivated by the work of De Giorgi, Nash, and Moser, in order to derive global and local supremum estimates, and a weak Harnack inequality.
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Ranner, Thomas. "Computational surface partial differential equations." Thesis, University of Warwick, 2013. http://wrap.warwick.ac.uk/57647/.

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Surface partial differential equations model several natural phenomena; for example in uid mechanics, cell biology and material science. The domain of the equations can often have complex and changing morphology. This implies analytic techniques are unavailable, hence numerical methods are required. The aim of this thesis is to design and analyse three methods for solving different problems with surface partial differential equations at their core. First, we define a new finite element method for numerically approximating solutions of partial differential equations in a bulk region coupled to surface partial differential equations posed on the boundary of this domain. The key idea is to take a polyhedral approximation of the bulk region consisting of a union of simplices, and to use piecewise polynomial boundary faces as an approximation of the surface and solve using isoparametric finite element spaces. We study this method in the context of a model elliptic problem. The main result in this chapter is an optimal order error estimate which is confirmed in numerical experiments. Second, we use the evolving surface finite element method to solve a Cahn- Hilliard equation on an evolving surface with prescribed velocity. We start by deriving the equation using a conservation law and appropriate transport formulae and provide the necessary functional analytic setting. The finite element method relies on evolving an initial triangulation by moving the nodes according to the prescribed velocity. We go on to show a rigorous well-posedness result for the continuous equations by showing convergence, along a subsequence, of the finite element scheme. We conclude the chapter by deriving error estimates and present various numerical examples. Finally, we stray from surface finite element method to consider new unfitted finite element methods for surface partial differential equations. The idea is to use a fixed bulk triangulation and approximate the surface using a discrete approximation of the distance function. We describe and analyse two methods using a sharp interface and narrow band approximation of the surface for a Poisson equation. Error estimates are described and numerical computations indicate very good convergence and stability properties.
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Fedrizzi, Ennio. "Partial differential equations and noise." Paris 7, 2012. http://www.theses.fr/2012PA077176.

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Dans ce travail, nous présentons quelques exemples des effets du bruit sur la solution d'une équation aux dérivées partielles dans trois contextes différents. Nous examinons d'abord deux équations aux dérivées partielles non linéaires dispersives, l'équation de Schrodinger non linéaire et l'équation de Korteweg - de | Vries. Nous analysons les effets d'une condition initiale aléatoire sur certaines solutions spéciales, les ! solitons. Le deuxième cas considéré est une équation aux dérive��es partielles linéaire, l'équation d'onde, avec conditions initiales aléatoires. Nous montrons qu'avec des conditions initiales aléatoires particulières c'est possible de réduire considérablement les coûts de stockage des données et de calcul d'un algorithme pour résoudre un problème inverse basé sur les mesures de la solution de cette équation au bord du domaine. Enfin, le troisième exemple considéré est celui de l'équation de transport linéaire avec un terme de dérive singulière. Nous allons montrer que l'ajout d'un terme de bruit multiplicatif interdit l'explosion | des solutions, et cela sous des hypothèses très faibles pour lesquelles dans le cas déterministe on peut avoir l'explosion de la solution à temps fini
In this work we present examples of the effects of noise on the solution of a partial differential equation in three different settings. We first consider random initial conditions for two nonlinear dispersive partial differential equations, the nonlinear Schrodinger equation and the Korteweg - de Vries equation, and analyze their effects on some special solutions, the soliton solutions. The second case considered is a linear PDE, the wave equation, with random initial conditions. We show that special random initial conditions allow to I substantially decrease the computational and data storage costs of an algorithm to solve the inverse problem based on the boundary measurements of the solution of this equation. Finally, the third example considered is that of the linear transport equation with a singular drift term, where we will show that the addition of a multiplicative noise term forbids the blow up of solutions, under very weak hypothesis for which we have finite-time blow up of solutions in the deterministic case
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Tarkhanov, Nikolai. "Unitary solutions of partial differential equations." Universität Potsdam, 2005. http://opus.kobv.de/ubp/volltexte/2009/2985/.

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Enstedt, Mattias. "Selected Topics in Partial Differential Equations." Doctoral thesis, Uppsala universitet, Matematiska institutionen, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-145763.

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This Ph.D. thesis consists of five papers and an introduction to the main topics of the thesis. In Paper I we give an abstract criteria for existence of multiple solutions to nonlinear coupled equations involving magnetic Schrödinger operators. In paper II we establish existence of infinitely many solutions to the quasirelativistic Hartree-Fock equations for Coulomb systems along with properties of the solutions. In Paper III we establish existence of a ground state to the magnetic Hartree-Fock equations. In Paper IV we study the Choquard equation with general potentials (including quasirelativistic and magnetic versions of the equation) and establish existence of multiple solutions. In Paper V we prove that, under some assumptions on its nonmagnetic counterpart, a magnetic Schrödinger operator admits a representation with a positive Lagrange density and we derive consequences of this property.
I den tryckta boken har förlag felaktigt angivits som Acta Universitatis Upsaliensis.
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Guo, Yujin. "Partial differential equations of electrostatic MEMS." Thesis, University of British Columbia, 2007. http://hdl.handle.net/2429/31315.

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Micro-Electromechanical Systems (MEMS) combine electronics with micro-size mechanical devices in the process of designing various types of microscopic machinery, especially those involved in conceiving and building modern sensors. Since their initial development in the 1980s, MEMS has revolutionized numerous branches of science and industry. Indeed, MEMS-based devices are now essential components of modern designs in a variety of areas, such as in commercial systems, the biomedical industry, space exploration, telecommunications, and other fields of applications. As it is often the case in science and technology, the quest for optimizing the attributes of MEMS devices according to their various uses, led to the development of mathematical models that try to capture the importance and the impact of the multitude of parameters involved in their design and production. This thesis is concerned with one of the simplest mathematical models for an idealized electrostatic MEMS, which was recently developed and popularized in a relatively recent monograph by J. Pelesko and D. Bernstein. These models turned out to be an incredibly rich source of interesting mathematical phenomena. The subject of this thesis is the mathematical analysis combined with numerical simulations of a nonlinear parabolic problem u[sub t] = Δu - [See Thesis for Equation] on a bounded domain of R[sup N] with Dirichlet boundary conditions. This equation models the dynamic deflection of a simple idealized electrostatic MEMS device, which consists of a thin dielectric elastic membrane with boundary supported at 0 above a rigid ground plate located at -1. When a voltage -represented here by λ- is applied, the membrane deflects towards the ground plate and a snap-through (touchdown) may occur when it exceeds a certain critical value λ* (pull-in voltage). This creates a so-called pull-in instability which greatly affects the design of many devices. In order to achieve better MEMS design, the elastic membrane is fabricated with a spatially varying dielectric permittivity profile f (x). The first part of this thesis is focussed on the pull-in voltage λ* and the quantitative and qualitative description of the steady states of the equation. Applying analytical and numerical techniques, the existence of λ* is established together with rigorous bounds. We show the existence of at least one steady state when λ < λ* (and when λ = λ* in dimension N < 8), while none is possible for λ > λ*. More refined properties of steady states--such as regularity, stability, uniqueness, multiplicity, energy estimates and comparison results--are shown to depend on the dimension of the ambient space and on the permittivity profile. The second part of this thesis is devoted to the dynamic aspect of the parabolic equation. We prove that the membrane globally converges to its unique maximal negative steady-state when λ ≤ λ*, with a possibility of touchdown at infinite time when λ = λ* and N ≥ 8. On the other hand, if λ > λ* the membrane must touchdown at finite time T , which cannot take place at the location where the permittivity profile f ( x ) vanishes. Both larger pull-in distance and larger pull-in voltage can be achieved by properly tailoring the permittivity profile. We analyze and compare finite touchdown times by using both analytical and numerical techniques. When λ > λ*, some a priori estimates of touchdown behavior are established, based on which, we can give a refined description of touchdown profiles by adapting recently developed self-similarity methods as well as center manifold analysis. Applying various analytical and numerical methods, some properties of the touchdown set - such as compactness, location and shape - are also discussed for different classes of varying permittivity profiles f (x).
Science, Faculty of
Mathematics, Department of
Graduate
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Keane, Therese Alison Mathematics &amp Statistics Faculty of Science UNSW. "Combat modelling with partial differential equations." Awarded By:University of New South Wales. Mathematics & Statistics, 2009. http://handle.unsw.edu.au/1959.4/43086.

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In Part I of this thesis we extend the Lanchester Ordinary Differential Equations and construct a new physically meaningful set of partial differential equations with the aim of more realistically representing soldier dynamics in order to enable a deeper understanding of the nature of conflict. Spatial force movement and troop interaction components are represented with both local and non-local terms, using techniques developed in biological aggregation modelling. A highly accurate flux limiter numerical method ensuring positivity and mass conservation is used, addressing the difficulties of inadequate methods used in previous research. We are able to reproduce crucial behaviour such as the emergence of cohesive density profiles and troop regrouping after suffering losses in both one and two dimensions which has not been previously achieved in continuous combat modelling. In Part II, we reproduce for the first time apparently complex cellular automaton behaviour with simple partial differential equations, providing an alternate mechanism through which to analyse this behaviour. Our PDE model easily explains behaviour observed in selected scenarios of the cellular automaton wargame ISAAC without resorting to anthropomorphisation of autonomous 'agents'. The insinuation that agents have a reasoning and planning ability is replaced with a deterministic numerical approximation which encapsulates basic motivational factors and demonstrates a variety of spatial behaviours approximating the mean behaviour of the ISAAC scenarios. All scenarios presented here highlight the dangers associated with attributing intelligent reasoning to behaviour shown, when this can be explained quite simply through the effects of the terms in our equations. A continuum of forces is able to behave in a manner similar to a collection of individual autonomous agents, and shows decentralised self-organisation and adaptation of tactics to suit a variety of combat situations. We illustrate the ability of our model to incorporate new tactics through the example of introducing a density tactic, and suggest areas for further research.
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Hofmanová, Martina. "Degenerate parabolic stochastic partial differential equations." Phd thesis, École normale supérieure de Cachan - ENS Cachan, 2013. http://tel.archives-ouvertes.fr/tel-00916580.

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In this thesis, we address several problems arising in the study of nondegenerate and degenerate parabolic SPDEs, stochastic hyperbolic conservation laws and SDEs with continues coefficients. In the first part, we are interested in degenerate parabolic SPDEs, adapt the notion of kinetic formulation and kinetic solution and establish existence, uniqueness as well as continuous dependence on initial data. As a preliminary result we obtain regularity of solutions in the nondegenerate case under the hypothesis that all the coefficients are sufficiently smooth and have bounded derivatives. In the second part, we consider hyperbolic conservation laws with stochastic forcing and study their approximations in the sense of Bhatnagar-Gross-Krook. In particular, we describe the conservation laws as a hydrodynamic limit of the stochastic BGK model as the microscopic scale vanishes. In the last part, we provide a new and fairly elementary proof of Skorkhod's classical theorem on existence of weak solutions to SDEs with continuous coefficients satisfying a suitable Lyapunov condition.
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Lloyd, David J. B. "Localised solutions of partial differential equations." Thesis, University of Bristol, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.434765.

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Lorz, Alexander Stephan Richard. "Partial differential equations modelling biophysical phenomena." Thesis, University of Cambridge, 2011. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.609381.

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Books on the topic "Partial differential equations"

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Taylor, Michael E. Partial differential equations. New York: Springer, 1996.

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Dezin, Aleksei A. Partial Differential Equations. Berlin, Heidelberg: Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/978-3-642-71334-7.

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Kevorkian, J. Partial Differential Equations. New York, NY: Springer New York, 2000. http://dx.doi.org/10.1007/978-1-4757-3266-5.

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Bellman, Richard, and George Adomian. Partial Differential Equations. Dordrecht: Springer Netherlands, 1985. http://dx.doi.org/10.1007/978-94-009-5209-6.

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Chern, Shiing-shen, ed. Partial Differential Equations. Berlin, Heidelberg: Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/bfb0082920.

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Cardoso, Fernando, Djairo G. de Figueiredo, Rafael Iório, and Orlando Lopes, eds. Partial Differential Equations. Berlin, Heidelberg: Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/bfb0100778.

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Jost, Jürgen. Partial Differential Equations. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-4809-9.

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Taylor, Michael E. Partial Differential Equations. New York, NY: Springer New York, 1996. http://dx.doi.org/10.1007/978-1-4684-9320-7.

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Epstein, Marcelo. Partial Differential Equations. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-55212-5.

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Jost, Jürgen. Partial Differential Equations. New York, NY: Springer New York, 2007. http://dx.doi.org/10.1007/978-0-387-49319-0.

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Book chapters on the topic "Partial differential equations"

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Gilbert, Robert P., George C. Hsiao, and Robert J. Ronkese. "Partial Differential Equations." In Differential Equations, 191–218. 2nd ed. Boca Raton: Chapman and Hall/CRC, 2021. http://dx.doi.org/10.1201/9781003175643-11.

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Bellman, Richard, and George Adomian. "Differential Quadrature." In Partial Differential Equations, 129–47. Dordrecht: Springer Netherlands, 1985. http://dx.doi.org/10.1007/978-94-009-5209-6_12.

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Jost, Jürgen. "Hyperbolic Equations." In Partial Differential Equations, 149–72. New York, NY: Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-4809-9_7.

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Vesely, Franz J. "Partial Differential Equations." In Computational Physics, 137–70. Boston, MA: Springer US, 1994. http://dx.doi.org/10.1007/978-1-4757-2307-6_5.

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Srinivas, Karkenahalli, and Clive A. J. Fletcher. "Partial Differential Equations." In Scientific Computation, 1–7. Berlin, Heidelberg: Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/978-3-642-58108-3_1.

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Fletcher, Clive A. J. "Partial Differential Equations." In Computational Techniques for Fluid Dynamics 1, 17–46. Berlin, Heidelberg: Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/978-3-642-58229-5_2.

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Dyke, Phil. "Partial Differential Equations." In Springer Undergraduate Mathematics Series, 123–43. London: Springer London, 2014. http://dx.doi.org/10.1007/978-1-4471-6395-4_5.

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Dyke, Philip P. G. "Partial Differential Equations." In Springer Undergraduate Mathematics Series, 111–28. London: Springer London, 2001. http://dx.doi.org/10.1007/978-1-4471-0505-3_5.

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Vesely, Franz J. "Partial Differential Equations." In Computational Physics, 125–55. Boston, MA: Springer US, 2001. http://dx.doi.org/10.1007/978-1-4615-1329-2_5.

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Shima, Hiroyuki, and Tsuneyoshi Nakayama. "Partial Differential Equations." In Higher Mathematics for Physics and Engineering, 539–62. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/b138494_17.

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Conference papers on the topic "Partial differential equations"

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Duteil, Nastassia Pouradier, Francesco Rossi, Ugo Boscain, and Benedetto Piccoli. "Developmental Partial Differential Equations." In 2015 54th IEEE Conference on Decision and Control (CDC). IEEE, 2015. http://dx.doi.org/10.1109/cdc.2015.7402696.

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CHOQUET-BRUHAT, YVONNE. "FUCHSIAN PARTIAL DIFFERENTIAL EQUATIONS." In Proceedings of the 14th Conference on WASCOM 2007. WORLD SCIENTIFIC, 2008. http://dx.doi.org/10.1142/9789812772350_0024.

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Guo, Boling, and Dadi Yang. "Nonlinear Partial Differential Equations and Applications." In International Conference on Nonlinear Partial Differential Equations and Applications. WORLD SCIENTIFIC, 1998. http://dx.doi.org/10.1142/9789814527989.

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Ufuktepe, Ünal. "Partial Differential Equations with webMathematica." In Proceedings of the Fifth International Mathematica Symposium. PUBLISHED BY IMPERIAL COLLEGE PRESS AND DISTRIBUTED BY WORLD SCIENTIFIC PUBLISHING CO., 2003. http://dx.doi.org/10.1142/9781848161313_0023.

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FAN, TIAN YOU. "QUASICRYSTALS AND PARTIAL DIFFERENTIAL EQUATIONS." In Statistical Physics, High Energy, Condensed Matter and Mathematical Physics - The Conference in Honor of C. N. Yang'S 85th Birthday. WORLD SCIENTIFIC, 2008. http://dx.doi.org/10.1142/9789812794185_0054.

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Vivona, Doretta, and Maria Divari. "Basic generated partial differential equations." In 2008 6th International Symposium on Intelligent Systems and Informatics (SISY 2008). IEEE, 2008. http://dx.doi.org/10.1109/sisy.2008.4664969.

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"Factorization of partial differential equations." In Уфимская осенняя математическая школа - 2022. 2 часть. Baskir State University, 2022. http://dx.doi.org/10.33184/mnkuomsh2t-2022-09-28.18.

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Francomano, Elisa, Adele Tortorici, Elena Toscano, Guido Ala, Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "Multiscale Particle Method in Solving Partial Differential Equations." In Numerical Analysis and Applied Mathematics. AIP, 2007. http://dx.doi.org/10.1063/1.2790115.

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MIYAKE, MASATAKE, and KUNIO ICHINOBE. "HIERARCHY OF PARTIAL DIFFERENTIAL EQUATIONS AND FUNDAMENTAL SOLUTIONS ASSOCIATED WITH SUMMABLE FORMAL SOLUTIONS OF A PARTIAL DIFFERENTIAL EQUATION OF NON KOWALEVSKI TYPE." In Differential Equations & Asymptotic Theory in Mathematical Physics. WORLD SCIENTIFIC, 2004. http://dx.doi.org/10.1142/9789812702395_0009.

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Ratier, Nicolas. "Analog computing of partial differential equations." In 2012 6th International Conference on Sciences of Electronic, Technologies of Information and Telecommunications (SETIT). IEEE, 2012. http://dx.doi.org/10.1109/setit.2012.6481928.

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Reports on the topic "Partial differential equations"

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Shearer, Michael. Systems of Hyperbolic Partial Differential Equations. Fort Belvoir, VA: Defense Technical Information Center, December 1994. http://dx.doi.org/10.21236/ada290287.

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Seidman, Thomas I. Nonlinear Systems of Partial Differential Equations. Fort Belvoir, VA: Defense Technical Information Center, September 1989. http://dx.doi.org/10.21236/ada217581.

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Arnold, Douglas, N, ed. Compatible Spatial Discretizations for Partial Differential Equations. Office of Scientific and Technical Information (OSTI), November 2004. http://dx.doi.org/10.2172/834807.

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Hyman, J. M., M. Shashkov, M. Staley, S. Kerr, S. Steinberg, and J. Castillo. Mimetic difference approximations of partial differential equations. Office of Scientific and Technical Information (OSTI), August 1997. http://dx.doi.org/10.2172/518902.

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Dalang, Robert C., and N. Frangos. Stochastic Hyperbolic and Parabolic Partial Differential Equations. Fort Belvoir, VA: Defense Technical Information Center, July 1994. http://dx.doi.org/10.21236/ada290372.

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Hale, Jack, Constantine M. Dafermos, John Mallet-Paret, Panagiotis E. Souganidis, and Walter Strauss. Dynamical Systems and Nonlinear Partial Differential Equations. Fort Belvoir, VA: Defense Technical Information Center, January 1989. http://dx.doi.org/10.21236/ada255356.

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Dafermos, Constantine M., John Mallet-Paret, Panagiotis E. Souganidis, and Walter Strauss. Dynamical Systems and Nonlinear Partial Differential Equations. Fort Belvoir, VA: Defense Technical Information Center, September 1993. http://dx.doi.org/10.21236/ada271514.

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Shearer, Michael. Systems of Nonlinear Hyperbolic Partial Differential Equations. Fort Belvoir, VA: Defense Technical Information Center, December 1997. http://dx.doi.org/10.21236/ada344449.

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Sharp, D. H., S. Habib, and M. B. Mineev. Numerical Methods for Stochastic Partial Differential Equations. Office of Scientific and Technical Information (OSTI), July 1999. http://dx.doi.org/10.2172/759177.

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Cai, X.-C. Scalable nonlinear iterative methods for partial differential equations. Office of Scientific and Technical Information (OSTI), October 2000. http://dx.doi.org/10.2172/15013129.

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