A finite time extinction profile and optimal decay for a fast diffusive doubly nonlinear equation

Abstract

In this article, we consider a fast diffusive type doubly nonlinear parabolic equation and study the extinction behavior of a solution at a finite time. We show the complete extinction of a weak solution with a nonnegative initial datum, that is, a weak solution is positive before a finite time and vanishes after it, and derive the optimal decay estimates of extinction. Our key ingredient of the proof is a nonlinear intrinsic scaling and the expansion of positivity.

Interior Holder Regularity and Infinite Time Extinction to a doubly Nonlinear Degenerate Parabolic Equations of Signed Solutions

“…In this context, we present the proposition regarding the extension of positivity. The complete proof can be found in [25]. Proposition 3.1.…”

“…We present a known lemma; cf. ( [1,11,25] for α > 1. This lemma is utilized in the proof of the subsequent lemma:…”