Decay estimates and blow up of solutions to a class of heat equations

2022/01/12 by Halder, Joydev, Tumuluri, Suman Kumar
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2201.04671

Abstract

In this article, we study a semi-linear heat equation with the nonlinearity which is the product of polynomial and logarithmic functions. Using the invariance of the potential well(s), we have established the global existence and exponential decay estimates of solutions in L² - norm without having any restriction on the exponent in the source term under suitable conditions on the initial data. Moreover, finite time blow up of solutions at subcritical, critical and supercritical initial energy levels is also discussed.

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