Viscosity Solutions to Second Order Parabolic PDEs on Riemannian Manifolds

被引：5

作者：

Zhu, Xuehong ^{[1
]}

机构：

[1] Nanjing Univ Aeronaut & Astronaut, Sch Sci, Nanjing 210016, Peoples R China

来源：

ACTA APPLICANDAE MATHEMATICAE | 2011年 / 115卷 / 03期

关键词：

Parabolic PDEs; Riemannian manifold; Viscosity solution; PARTIAL-DIFFERENTIAL-EQUATIONS;

D O I：

10.1007/s10440-011-9621-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this work we consider viscosity solutions to second order parabolic PDEs u (t) +F(t,x,u,du,d (2) u)=0 defined on complete Riemannian manifolds with boundary conditions. We prove comparison, uniqueness and existence results for the solutions. Under the assumption that the manifold M has nonnegative sectional curvature, we get the finest results. If one additionally requires F to depend on d (2) u in a uniformly continuous manner, the assumptions on curvature can be thrown away.

引用

页码：279 / 290

页数：12

共 50 条

[41] Solutions of Second-Order PDEs with First-Order Quotients
E. Schneider
Lobachevskii Journal of Mathematics, 2020, 41 : 2491 - 2509
[42] Pseudo-almost periodic viscosity solutions of second-order nonlinear parabolic equations
Zhang, Shilin
Gao, Zhen
Piao, Daxiong
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2011, 74 (18) : 6970 - 6980
[43] Solutions of Second-Order PDEs with First-Order Quotients
Schneider, E.
LOBACHEVSKII JOURNAL OF MATHEMATICS, 2020, 41 (12) : 2491 - 2509
[44] Global existence of solutions to parabolic Monge-Ampere equations on Riemannian manifolds
Ru, Qiang
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2015, 116 : 145 - 152
[45] ON THE UPPER ESTIMATES OF FUNDAMENTAL-SOLUTIONS OF PARABOLIC EQUATIONS ON RIEMANNIAN-MANIFOLDS
LI, JY
SHAO, X
CHINESE ANNALS OF MATHEMATICS SERIES B, 1995, 16 (01) : 119 - 130
[46] Second order optimality conditions for optimal control problems on Riemannian manifolds*
Cui, Qing
Deng, Li
Zhang, Xu
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 2019, 25
[47] Second-order multivalued stochastic differential equations on Riemannian manifolds
Bernardin, F
Schatzman, M
Lamarque, CH
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2004, 460 (2051): : 3095 - 3121
[48] DIFFERENTIAL OPERATORS OF SECOND-ORDER ON RIEMANNIAN MANIFOLDS WITH NONPOSITIVE CURVATURE
SIMON, U
COLLOQUIUM MATHEMATICUM, 1974, 31 (02) : 223 - 229
[49] Separation Problem for Second Order Elliptic Differential Operators on Riemannian Manifolds
Atia, H. A.
JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS, 2015, 19 (02) : 229 - 240
[50] A Rate of Convergence of Weak Adversarial Neural Networks for the Second Order Parabolic PDEs
Jiao, Yuling
Yang, Jerry Zhijian
Yuan, Cheng
Zhou, Junyu
COMMUNICATIONS IN COMPUTATIONAL PHYSICS, 2023, 34 (03) : 813 - 836

← 1 2 3 4 5 →