Bibliographies thématiques / Hamilton-Jacobi equations with unbounded data

Littérature scientifique sur le sujet « Hamilton-Jacobi equations with unbounded data »

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Publié le 11 mars 2023

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Articles de revues sur le sujet "Hamilton-Jacobi equations with unbounded data"

Cosso, Andrea, Huyên Pham et Hao Xing. « BSDEs with diffusion constraint and viscous Hamilton–Jacobi equations with unbounded data ». Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 53, n^o 4 (novembre 2017) : 1528–47. http://dx.doi.org/10.1214/16-aihp762.

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Nadolski, Adam. « Hamilton–Jacobi functional differential equations with unbounded delay ». Annales Polonici Mathematici 82, n^o 2 (2003) : 105–26. http://dx.doi.org/10.4064/ap82-2-2.

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Zălinescu, Adrian. « Second order Hamilton–Jacobi–Bellman equations with an unbounded operator ». Nonlinear Analysis : Theory, Methods & ; Applications 75, n^o 13 (septembre 2012) : 4784–97. http://dx.doi.org/10.1016/j.na.2012.03.028.

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Tataru, Daniel. « Viscosity solutions of Hamilton-Jacobi equations with unbounded nonlinear terms ». Journal of Mathematical Analysis and Applications 163, n^o 2 (janvier 1992) : 345–92. http://dx.doi.org/10.1016/0022-247x(92)90256-d.

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Barles, Guy, et Joao Meireles. « On unbounded solutions of ergodic problems in ℝmfor viscous Hamilton–Jacobi equations ». Communications in Partial Differential Equations 41, n^o 12 (14 novembre 2016) : 1985–2003. http://dx.doi.org/10.1080/03605302.2016.1244208.

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Armstrong, Scott N., et Panagiotis E. Souganidis. « Stochastic homogenization of Hamilton–Jacobi and degenerate Bellman equations in unbounded environments ». Journal de Mathématiques Pures et Appliquées 97, n^o 5 (mai 2012) : 460–504. http://dx.doi.org/10.1016/j.matpur.2011.09.009.

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Brändle, Cristina, et Emmanuel Chasseigne. « On unbounded solutions of ergodic problems for non-local Hamilton–Jacobi equations ». Nonlinear Analysis 180 (mars 2019) : 94–128. http://dx.doi.org/10.1016/j.na.2018.09.015.

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Shimano, K. « A Class of HamiltonJacobi Equations with Unbounded Coefficients in Hilbert Spaces ». Applied Mathematics and Optimization 45, n^o 1 (1 janvier 2002) : 75–98. http://dx.doi.org/10.1007/s00245-001-0028-4.

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Qiu, Hong, et Jiongmin Yong. « Hamilton–Jacobi equations and two-person zero-sum differential games with unbounded controls ». ESAIM : Control, Optimisation and Calculus of Variations 19, n^o 2 (23 janvier 2013) : 404–37. http://dx.doi.org/10.1051/cocv/2012015.

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Stokols, Logan F., et Alexis F. Vasseur. « De Giorgi techniques applied to Hamilton–Jacobi equations with unbounded right-hand side ». Communications in Mathematical Sciences 16, n^o 6 (2018) : 1465–87. http://dx.doi.org/10.4310/cms.2018.v16.n6.a1.

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Thèses sur le sujet "Hamilton-Jacobi equations with unbounded data"

GOFFI, ALESSANDRO. « Topics in nonlinear PDEs : from Mean Field Games to problems modeled on Hörmander vector fields ». Doctoral thesis, Gran Sasso Science Institute, 2019. http://hdl.handle.net/20.500.12571/9808.

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This thesis focuses on qualitative and quantitative aspects of some nonlinear PDEs arising in optimal control and differential games, ranging from regularity issues to maximum principles. More precisely, it is concerned with the analysis of some fully nonlinear second order degenerate PDEs over Hörmander vector fields that can be written in Hamilton-Jacobi-Bellman and Isaacs form and those arising in the recent theory of Mean Field Games, where the prototype model is described by a coupled system of PDEs involving a backward Hamilton-Jacobi and a forward Fokker-Planck equation. The thesis is divided in three parts. The first part is devoted to analyze strong maximum principles for fully nonlinear second order degenerate PDEs structured on Hörmander vector fields, having as a particular example fully nonlinear subelliptic PDEs on Carnot groups. These results are achieved by introducing a notion of subunit vector field for these nonlinear degenerate operators in the spirit of the seminal works on linear equations. As a byproduct, we then prove some new strong comparison principles for equations that can be written in Hamilton-Jacobi-Bellman form and Liouville theorems for some second order fully nonlinear degenerate PDEs. The second part of the thesis deals with time-dependent fractional Mean Field Game systems. These equations arise when the dynamics of the average player is described by a stable Lévy process to which corresponds a fractional Laplacian as diffusion operator. More precisely, we establish existence and uniqueness of solutions to such systems of PDEs with regularizing coupling among the equations for every order of the fractional Laplacian $sin(0,1)$. The existence of solutions is addressed via the vanishing viscosity method and we prove that in the subcritical regime the equations are satisfied in classical sense, while if $sleq1/2$ we find weak energy solutions. To this aim, we develop an appropriate functional setting based on parabolic Bessel potential spaces. We finally show uniqueness of solutions both under the Lasry-Lions monotonicity condition and for short time horizons. The last part focuses on the regularizing effect of evolutive Hamilton-Jacobi equations with Hamiltonian having superlinear growth in the gradient and unbounded right-hand side. In particular, the analysis is performed both for viscous Hamilton-Jacobi equations and its fractional counterpart in the subcritical regime via a duality method. The results are accomplished exploiting the regularity of solutions to Fokker-Planck-type PDEs with rough velocity fields in parabolic Sobolev and Bessel potential spaces respectively.

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ADDONA, DAVIDE. « Parabolic operators with unbounded coefficients with applications to stochastic optimal control games ». Doctoral thesis, Università degli Studi di Milano-Bicocca, 2015. http://hdl.handle.net/10281/76535.

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The aim of this thesis is to improve some results on parabolic Cauchy problems with unbounded coefficients and their connection with stochastic optimal games. In the first part we summarize the recent results on parabolic operators with unbounded coefficients and on stochastic optimal control problem. In particular, in the matter of analyitic results, we recall the main exstence and uniqueness theorems for parabolic Cauchy problems with unbounded coefficients, the gradient estimates for the associated evolution operator, and its continuity and compactness properties. About the stochastic part, we briefly show the strong and weak formulation, which are the settings where the stochastic control problems are located, and we introduce the backward stochastic differential equations, which allow to connect a semilinear Cauchy problem with a class of stochastic control problem. In the second part we prove the existence and uniqueness of a mild solution to a semilinear parabolic Cauchy problem of Hamilton-Jacobi-Bellman (HJB) type. Moreover, we show that the solution to a Forward Backward Stochastic Differential Equation (FBSDE) can be expressed in terms of the solution to the HJB equation. Combining HJB equation and FBSDE, we show that, for a class of stochastic control problemin weak formulation, there exists an optimal control, and by means of the regularity of the solution to the HJB equation, we can identify the feedback law. The third part of the thesis is devoted to the study of a class of system of nonautonomous linear parabolic equations with unbounded coefficients, coupled both at first and zero order. We provide sufficient conditions which guarantee the existence and uniqueness of a classical solution to the Cauchy problem, and throughout this classical solution we define an evolution operator on the space of bounded and continuous functions. Further, we prove continuity properties of the evolution operator and that, under additional hypotheses, it is compact on the space of bounded and continuous functions. In the last chapter, we deal with a semilinear system of parabolic equations and its application to differential games. At first, we prove the existence of a mild solution to the system by an approximation argument. Throughout this mild solution, we show the existence of an adapted solution to a system of FBSDE which allows us to prove the existence of a Nash equilibrium for a class of differential games.

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FESTA, ADRIANO. « Analysis and Approximation of Hamilton Jacobi equations on irregular data ». Doctoral thesis, 2012. http://hdl.handle.net/11573/917536.

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We will present some numerical schemes for some non classical Hamilton-Jacobi equations. We will consider an Eikonal equation with discontinuous coefficients. In this case, through a particular condition on the discontinuities we can preserve a comparison principle for the solutions. We will introduce ans study a semiLagrangian numerical scheme also deriving error bounds. Another case which we will present is an eikonal equation on a graph. We will briefly present the notion of viscosity solution in this situation introduced by Camilli and al. in 2010 and we will build a numerical approximation for it. Some numerical solutions for the Shape-from-Shading problem and for an optimal control problem on a domain with constraints will be presented.

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Chapitres de livres sur le sujet "Hamilton-Jacobi equations with unbounded data"

« 6. Numerical Solution Of The Simple Monge–Ampère Equation With Nonconvex Dirichlet Data On Nonconvex Domains ». Dans Hamilton-Jacobi-Bellman Equations, 129–42. De Gruyter, 2018. http://dx.doi.org/10.1515/9783110543599-006.

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Actes de conférences sur le sujet "Hamilton-Jacobi equations with unbounded data"

Claudel, Christian G., et Alexandre M. Bayen. « Linear and quadratic programming formulations of data assimilation or data reconciliation problems for a class of Hamilton-Jacobi equations ». Dans 2010 American Control Conference (ACC 2010). IEEE, 2010. http://dx.doi.org/10.1109/acc.2010.5530615.

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