Existence and nonexistence of global solutions of quasilinear parabolic equations. (Q1396383)

A critical exponent for the global existence of nontrivial nonnegative solutions of the equation \(u_t=\Delta u^m + K(x)u^p\) in the whole space is found. It is assumed that \(1\leq m<p\) and that \(K(x)\geq 0\) behaves like \(| x| ^\sigma\) as \(| x| \to\infty\) in some cone \(D\), \(K(x)=0\) in the complement of \(D\).