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We prove the existence of a critical Fujita exponent for a non-homogeneoussemilinear heat equation which involves degenerate coefficients. Moreprecisely, in order to give a rather complete theory, we focus on two types ofweights $w(x)=|x_1|^a$ or $w(x)=|x|^b$ where $a, b>0$ in a suitable range. Thecoefficients under consideration admit either a singularity at the origin or aline of singularities. In the latter case, the problem is related to thefractional Laplacian.

Critical Fujita exponent for a semilinear heat equation with degenerate coefficients