The Initial-boundary Value Problem For A Class Of Fourth-order Parabolic Systems With Memory Terms

The initial-boundary value problem of a kind of fourth order parabolic equations(?),is considered in this paper,where?(?)R~n is a bounded domain with sufficiently smooth boundary.g_i(t)(i=1,2)are non-negative functions defined on R~+.A_i(x,t)(i=1,2)are generalized Lewis functions.The main contents of this thesis are summarized as follow.In the first Chapter,some backgrounds,known methods and the main results of this paper are given.In the second Chapter,the definitions of weak solution,energy function and some lemmas are given.In the third Chapter,the existence of global solutions for this problem is proved by constructing a stable set.Based on the integral inequality and Sobolev embedding theorem,it is confirmed that energy of weak solution decays with exponential rate.In the fourth Chapter,it is also proved that the weak solution will blow-up with positive and negative initial energy by applying convex method,and the lower bound for the life-span is given.