Blow-up And Decay For A Class Of Parabolic Equation

In this thesis,we consider the following problem{ut+?(|?u|p-2?u)=-div(|?u|q-2?ulog|?u|),x??,t>0,u(x,t)=?u(x,t)=0,x??,t>0,u(x,0)=u0(x),x??,where ??Rn is a bounded domain,with smooth boundary ?,p,q are constants such that 2<p<q<p(1+2/n+2)and u0?(w1,p0(?)?W2,p(?))\{0}.In this thesis,we study the parabolic equation by using the method of potential wells.We have proved that there is a unique local weak solution and a unique global weak solution with algebraic decay.We also obtain results of the energy inequality and the finite time blow-up for weak solutions.