Existence of viscosity solutions of Hamilton-Jacobi equations
Existence of viscosity solutions of Hamilton-Jacobi equations
复制标题
Hamilton-Jacobi方程粘度解的存在性
DOI：
10.1016/0022-0396(85)90084-1
复制
发表时间：
1985
影响因子：
2.4
通讯作者：
P. Souganidis
中科院分区：
文献类型：
--
作者：
P. Souganidis
Hamilton-Jacobi型方程出现在许多应用领域，包括变分法、控制理论和微分对策。最近M。G. Crandall和P. - L. Lions（Trans.Amer.Math.Soc.277（1983），1-42）介绍了这类方程的“粘性”解，并证明了这类解的唯一性。本文讨论了这些解决方案的存在性密切相关的假设，保证唯一性。
Equations of Hamilton-Jacobi type arise in many areas of application, including the calculus of variations, control theory and differential games. Recently M. G. Crandall and P.-L. Lions (Trans. Amer. Math. Soc.277(1983), 1–42) introduced the class of “viscosity” solutions of these equations and proved uniqueness within this class. This paper discusses the existence of these solutions under assumptions closely related to the ones which guarantee the uniqueness.