Remarks on the existence and uniqueness of unbounded viscosity solutions of Hamilton-Jacobi equations. (English) Zbl 0678.35009

Crandall, Michael G.; Lions, Pierre-Louis

Ill. J. Math. 31, 665-688 (1987).

This paper deals with existence and uniqueness questions for unbounded viscosity solutions of general first-order Hamilton-Jacobi equations. The growth condition on the gradient dependence includes power functions. The growth of solutions is limited by exponential functions. Some cases are presented in which non-uniqueness is possible and the existence of minimal solutions is given. The Cauchy problem is treated also, in particular the case without conditions at infinity.

Reviewer: S.Lenhart

MSC:

35F30	Boundary value problems for nonlinear first-order PDEs
35A05	General existence and uniqueness theorems (PDE) (MSC2000)

Keywords:

existence; uniqueness; viscosity solutions; first-order Hamilton-Jacobi equations; Cauchy problem