Critical Fujita exponent for a semilinear heat equation with degenerate coefficients

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 $w(x)=|x_1{|}^a$ 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.

24pages. arXiv admin note: substantial text overlap with arXiv:1711.11187 by other authors