Finite extinction for a doubly nonlinear parabolic equation of fast diffusion type

Abstract

Purpose – The purpose of this paper is to find a doubly nonlinear parabolic equation of fast diffusion in a bounded domain. Design/methodology/approach – For positive and bounded initial data, the authors study the initial zero-boundary value problem. Findings – The findings of this study showed the complete extinction of a continuous weak solution at a finite time. Originality/value – The extinction time is studied earlier but for the Laplacian case. The authors presented the finite extinction time for the case of p-Laplacian.

Keywords

• Doubly nonlinear equation
• Degenerate and singular equation
• Sobolev critical case
• Finite time extinction