Stability of weak solutions of a non-Newtonian polytropic filtration equation

Abstract

We study a non-Newtonian polytropic filtration equation with a convection term. We introduce new type of weak solutions and show the existence of weak solutions. We show that when $\int_{\Omega} [a(x)]^{-1(p-1)}dx<\infty$, the stability of weak solutions is based on the usual initial-boundary value conditions. When $1<p<2$, under the given conditions on the diffusion coefficient and the convection term, the stability of weak solutions can be proved without any boundary value condition. In particular, the stability results are presented based on the given optimal boundary value condition.

Keywords

• Weak solution
• convection term
• stability
• boundary value condition