拟线性抛物型方程组广义解的可积性

Integrabilities for Generalized Solutions of Quasi-linear Parabolic Systems

在适当条件下证明形如(1)的拟线性抛物型方程组的广义解u满足其中θ为(0,1)中的某个数,γ>0可以任意。

Let G be a bounded Lipschitz domain in E^nQ= G×(O,T) with finite T>O. It is proved that under suitable conditions the solution of the following equation Vt∈(O,T), v∈W_2~1(O,T,L_2(G))∩L_2(O,T,W_2~1(G)), u∈C(O,T,L_2(G))∩L(O,T,W_2~1(G)), has the following integrabilities: and where θ is a real number between 0 and 1 and γ>0 may be arbitrary.