Critical Fujita exponent for a semilinear heat equation with degenerate coefficients

2022/11/09 by Hu, Xi, Tang, Lin
#35B33 #35K58 #35K65 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2212.12491

Abstract

We prove the existence of a critical Fujita exponent for a non-homogeneous semilinear heat equation which involves degenerate coefficients. More precisely, in order to give a rather complete theory, we focus on two types of weights w(x)=|x₁|^a or w(x)=|x|^b where a, b>0 in a suitable range. The coefficients under consideration admit either a singularity at the origin or a line of singularities. In the latter case, the problem is related to the fractional Laplacian.

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