L^{infty } decay estimates of solutions of nonlinear parabolic equation

Hui Wang,Caisheng Chen

doi:10.1186/s13661-020-01480-8

Abstract

In this paper, we are interested in L^{infty } decay estimates of weak solutions for the doubly nonlinear parabolic equation and the degenerate evolution m-Laplacian equation not in the divergence form. By a modified Moser’s technique we obtain L^{infty } decay estimates of weak solutiona.

Highlights

1 Introduction In this paper, we are interested in the L∞ decay estimate of the solution for the initialboundary-value problem of the nonlinear parabolic equation in the divergence form
As in [20], we introduce a new independent variable u = |v|β–1v
As in the proof of Theorem 1, we can show that there exist bounded sequences {ξn} and {λn} such that u(t) pn ≤ ξnt–λn t > 0, in which λn → λ and ξn ≤ C0

Summary

Introduction

We are interested in the L∞ decay estimate of the solution for the initialboundary-value problem of the nonlinear parabolic equation in the divergence form.

Wang and Chen Boundary Value Problems

It is not difficult to show that λn