Global Existence And Extinction For A Degenerate Nonlinear Diffusion Problem With Nonlinear Gradient Term And Absorption

This paper is devoted to the study of the initial boundary problem for aclass degenerate nonlinear diffusion equation with gradient term and absorptionof the form u_t=â–³u^m-λu^p+|(?)u^α|^q on Q=Ω×(0,∞),where m≥1,p>0,λ>0,1≤q<2,α>m/2,Ω(?)R^N is a bounded domain．The initial datau(x,0)=u₀(x)∈L^∞(Ω)with u₀(x)≥0．We obtain existence and extinctionin finite time of global weak solutions for above-mentioned problem on someassumption for m,p,q,α,u₀．...