Localized peaking regimes for quasilinear doubly degenerate parabolic equations

TL;DR

This paper investigates singular peaking behaviors in quasilinear doubly degenerate parabolic equations, providing precise energy-based estimates of solution profiles near peaking times.

Contribution

It introduces a new energy method approach to analyze peaking regimes and derives detailed estimates of solution behavior in these regimes.

Findings

Established energy-based estimates for solution profiles near peaking times

Identified conditions under which singular peaking occurs in these equations

Provided a framework for analyzing degenerate parabolic equations with peaking phenomena

Abstract

Regimes with a singular peaking for a wide class of quasilinear second order parabolic equations are studied. On the basis of energy methods, precise estimates of a final profile of a weak solution in a neighborhood of the peaking time are established depending on the rate of increase of a global energy of this solution. Key words: quasilinear parabolic equations, peaking regimes, energy solutions.