Viscosity solutions for Hamilton-Jacobi equations with unbounded nonlinear term: A simplified approach. (English) Zbl 0810.34060

Tataru, Daniel

J. Differ. Equations 111, No. 1, 123-146 (1994).

In a previous work [J. Math. Anal. Appl. 163, No. 2, 345-392 (1992; Zbl 0757.35034)] the author introduced a notion of viscosity solution for Hamilton-Jacobi equations with unbounded nonlinear term and proved existence and comparison results for both stationary problems and Cauchy problems.
The purpose of the present paper is to define in a simpler and more intuitive way the class of so-called viscosity solutions for Hamilton- Jacobi equations with unbounded nonlinear term and to prove that two definitions are equivalent. The new definition seems to be closer to the approaches of M. G. Crandall and P. L. Lions and to simplify some proofs and extensions.

Reviewer: M.A.Vivaldi (Roma)

MSC:

34G20

Nonlinear differential equations in abstract spaces

Keywords:

viscosity solutions; Hamilton-Jacobi equations with unbounded nonlinear term

Citations:

Zbl 0757.35034