Existence and nonexistence of global solutions of quasilinear parabolic equations
Existence and nonexistence of global solutions of quasilinear parabolic equations
We consider nonnegative solutions to the Cauchy problem for the quasilinear parabolic equations ut=Δum+K(x)up where x∈RN, 1≤m<p and K(x)≥0 has the following properties: K(x)-|x|σ(-∞≤σ<∞) as |x|→∞ in some cone D and K(x)=0 in the complement of D, where for σ=-∞ we define that K(x) has a compact support. We find …