New Fujita type results for quasilinear parabolic differential inequalities with gradient dissipation terms

Abstract

This paper deals with the new Fujita type results for Cauchy problem of a quasilinear parabolic differential inequality with both a source term and a gradient dissipation term. Specially, nonnegative weights may be singular or degenerate. Under the assumption of slow decay on initial data, we prove the existence of second critical exponents $ \mu^{*} $, such that the nonexistence of solutions for the inequality occurs when $ \mu < \mu^{*} $.

Keywords

• parabolic differential inequalities
• nonexistence of solutions
• global solutions
• second critical exponent