Global Existence And Blow-up Of Solutions To P-laplace Equations With Logarithmic Sources

The aim of this thesis is to study the global existence and blow up of solutions to parabolic problems involving logarithmic nonlinearity and p-Laplace operator.Our main problems studied is as followsAt first,we give some necessary preliminaries and our main results.Subsequently,we apply the revised well potential method,energy estimates,argument by contradiction and embedding inequalities etc.to prove that the solution globally exists or blows up at infinite.Specifically speaking,based on the relationship between the initial energy and M=1/p2?p2e/n???p?n/p as well as the nonnegativity of I?u₀?=??|?u₀|pdx-??|u₀|plog|u₀|dx,we obtain the following conclusions:Theorem 1.If u₀?x?? W₀^1,p???,J?u₀?<M,I?u₀?? 0.Then the problem?0.1?has a global weak solution u ? L^?(0,+?;W₀^1,p???)with ut ?L²?0,+?;L²????.Moreover,we have the following bounded estimate,Theorem 2.If u₀?x?? W₀^1,p???,J?u₀?=M,I?u₀?? 0.Then the problem?0.1?has a global weak solution u ? L^??0,+?;W01.p????with u1 ?L²?0,+?;L²????.Moreover,if I?u₀?>0,then for any given sufficiently small positive number y,there exists t>0 such thatTheorem 3.If u₀?x?? W₀^1,p???,J?u₀?? M,I?u₀?<0.Then the weak solution u = u?x,t?of the problem?0.1?blows up at +?,i.e.