On the nonexistence of positive solutions to nonlinear degenerate parabolic equations with singular coefficients

Abstract

In this paper, we shall investigate the nonexistence of positive solutions for the following nonlinear parabolic partial differential equations:

Here, Ω is a Carnot–Carathéodory metric ball in and . The critical exponent m∗ is found, and the nonexistence results are proved for m∗≤ m<1.

Keywords:

• Nonlinear parabolic equations
• Positive solutions
• Hardy-type inequality
• AMS Subject Classifications: 35K55
• 35H10
• 35K65
• 35R05