Asymptotic behavior of solutions for a doubly degenerate parabolic non-divergence form equation

Abstract

This paper is concerned with the asymptotic behavior of a doubly degenerate parabolic equation in non-divergence form. The proofs are divided into three cases according to exponent values of the source, and, by using different methods, we prove the stability of the steady states. We also expand the discussion of asymptotic stability for equations with the periodic source.