Global nonexistence of solutions to degenerate parabolic equations in unbounded domains

In this work, we study the global nonexistence of weak solutions for the doubly degenerate parabolic equation (uk)t=div(|∇u|m−2∇u)+h(x)up+H(x)|∇u|q with zero boundary conditions in an unbounded domain Ω⊂RNΩ⊂RN. By a test function method, we prove that the problem has no global solution if the initial data u0(x)u0(x) satisfies lim inf|x|→∞(u0(x)|x|m+μ1p−m+1)≥C0 for some C0>0C0>0.