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arXiv · 2201.04671

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

Joydev Halder·Suman Kumar Tumuluri
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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 $L^2$ - 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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Joydev Halder, Suman Kumar Tumuluri. 2022-01-12. Decay estimates and blow up of solutions to a class of heat equations. https://arxiv.org/abs/2201.04671

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