The variational approach to Hamilton-Jacobi equations driven by a Gaussian noise

被引：0

作者：

Barbu, Viorel ^{[1
,2
]}

机构：

[1] Alexandru Ioan Cuza Univ, Iasi, Romania

[2] Romanian Acad, Octav Mayer Inst Math, Iasi, Romania

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2013年 / 255卷 / 11期

关键词：

Hamilton-Jacobi equation; Brownian motion; Viscosity solution; Stochastic process; VISCOSITY SOLUTIONS; INTEGRALS;

D O I：

10.1016/j.jde.2013.07.044

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The global existence and uniqueness of viscosity solutions to the Cauchy problem for the Hamilton-Jacobi equations in RN driven by additive and multiplicative Wiener processes are studied for convex Hamiltonians via variational techniques. The finite speed of propagation is also established in the multiplicative noise case for equations with Lipschitzian Hamiltonians. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：3832 / 3847

页数：16

共 50 条

[1] Variational solutions of coupled Hamilton-Jacobi equations
Loreti, P
Caffarelli, GV
APPLIED MATHEMATICS AND OPTIMIZATION, 2000, 41 (01): : 9 - 24
[2] HAMILTON-JACOBI EQUATIONS IN HILBERT-SPACES - VARIATIONAL AND SEMIGROUP APPROACH
BARBU, V
DAPRATO, G
ANNALI DI MATEMATICA PURA ED APPLICATA, 1985, 142 : 303 - 349
[3] STOCHASTIC AND VARIATIONAL APPROACH TO FINITE DIFFERENCE APPROXIMATION OF HAMILTON-JACOBI EQUATIONS
Soga, Kohei
MATHEMATICS OF COMPUTATION, 2020, 89 (323) : 1135 - 1159
[4] Regularization by noise for stochastic Hamilton-Jacobi equations
Gassiat, Paul
Gess, Benjamin
PROBABILITY THEORY AND RELATED FIELDS, 2019, 173 (3-4) : 1063 - 1098
[5] Variational optimisation by the solution of a series of Hamilton-Jacobi equations
Venkatesh, PK
Petzold, LR
Carr, RW
Cohen, MH
Dean, AM
PHYSICA D, 2001, 154 (1-2): : 15 - 25
[6] A REPRESENTATIONAL FORMULA FOR VARIATIONAL SOLUTIONS TO HAMILTON-JACOBI EQUATIONS
McCaffrey, David
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2012, 11 (03) : 1205 - 1215
[7] Gaussian beams, the hamilton-jacobi equations, and finsler geometry
Katchalov A.P.
Journal of Mathematical Sciences, 2005, 127 (6) : 2374 - 2388
[8] A Hamilton-Jacobi approach to neural field equations
Tao, Wen
Li, Wan-Tong
Sun, Jian-Wen
JOURNAL OF DIFFERENTIAL EQUATIONS, 2025, 422 : 659 - 695
[9] A Hamilton-Jacobi approach to nonlocal kinetic equations
Loy, Nadia
Perthame, Benoit
NONLINEARITY, 2024, 37 (10)
[10] ON C0-VARIATIONAL SOLUTIONS FOR HAMILTON-JACOBI EQUATIONS
Bernardi, Olga
Cardin, Franco
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2011, 31 (02) : 385 - 406

← 1 2 3 4 5 →