Existence of Viscosity Solutions for Weakly Coupled Cooperative Parabolic Systems with Fully Nonlinear Principle Part

Abstract

In this paper, the existence of viscosity solutions for weakly coupled, degenerate, and cooperative parabolic systems is studied in a bounded domain. In particular, we consider the viscosity solutions of parabolic systems with fully nonlinear degenerated principal symbol and linear coupling part. The maximum principle theorem is given as well.

Keywords

• degenerate parabolic quasi-monotone systems
• viscosity solutions
• maximum principle
• existence