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Local well-posedness and blow-up for an inhomogeneous nonlinear heat equation
Journal article   Peer reviewed

Local well-posedness and blow-up for an inhomogeneous nonlinear heat equation

Rasha Alessa, Aisha Alshehri, Haya Altamimi and Mohamed Majdoub
Mathematical methods in the applied sciences, Vol.43(8), pp.5264-5272
30/05/2020
DOI: https://doi.org/10.1002/mma.6266

Abstract

Mathematics Mathematics, Applied Physical Sciences Science & Technology
In this paper, we consider the nonlinear heat equation with inhomogeneous nonlinearity ut-Delta u=a(x)f(u) where f:R -> R having either a polynomial growth or exponential growth, and a:RN -> R is a function satisfying some assumptions to be stated later. We first prove the local well-posedness in suitable Lebesgue spaces when a belongs to some Lebesgue space and f has polynomial growth. We also obtain some blow-up results.

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