Research On The Blow-up, Quenching And Global Existence Of The Solutions Of Two Types Of Nonlinear Parabolic Equations

In this work,we consider the global existence,blow-up and extinction behavior of solutions of two kinds of nonlinear parabolic partial differential equations.In chapter 1,we consider the blow-up and extinction behavior of solutions to a class of p-biharmonic parabolic equation where D is ? ×?0,t*?,S in????×?0,+??,????R^N?N?1?? is a bounded domain with smooth boundary????,f:[0,?)?[0,?)is a locally Lipschitz function,m???represents the Lebesgue measure of the domain ?,? ? 0,max[1,2N/N+4]<p ?2,u₀?x?? L^????\?W^2,p?Q?.In chapter 2,we consider the global existence and non-extinction properties of solutions to a nonlocal parabolic equation where ? is a bounded domain of R^N?N ? 2?with smooth boundary????.