Localization for the evolution p-Laplacian equation with strongly nonlinear source term

In this paper we study the strict localization for the p  -Laplacian equation with strongly nonlinear source term. Let u:=u(x,t)u:=u(x,t) be a solution of the Cauchy problemut=div(|∇u|p−2∇u)+uq,u(x,0)=u0(x), where (x,t)∈RN×(0,T)(x,t)∈RN×(0,T), N⩾1N⩾1 and p>2p>2. When q⩾p−1q⩾p−1, we prove that if the initial data u0(x)u0(x) has a compact support, then the solution u(⋅,t)u(⋅,t) has also compactly support. Moreover, when 1