The Existence Of Global Weak Solutions And Attractors For Anisotropic Parabolic P-Laplacian Equations

This dissertations investigates the global existence and asymptotic behavior for anisotropic parabolic p-Laplacian equation in Rn.The following anisotropic parabol-ic p-Laplacian equations are considered where ?>0,1<r<?,1<pi<n(n>2),i?{1,…,n}.The nonlinearity f is a Caratheodory function and satisfies subcritical growth condition.By using the classical Galerkin approximation and standard domain expansion technique,the global weak solution of the problem is proved.At the same time,we prove existence of global attractors for the anisotropic parabolic equation in L2(Rn)? Lr(Rn)via the ?-limit compact of multi-valued semigroups.