一类带记忆项的非线性弹性杆方程初边值问题

摘要

在给定的Sobolve空间中,利用Galerkin方法证明了一类带记忆项的非线性演化方程整体弱解的存在性.其中非线性项具有临界增长指数,记忆项满足指数衰减条件.%The existence of integral weak solutions for a class of nonlinear evolution equation with memory term in given Sobolve space is proved with Galerkin method.The nonlinear term in the equation have a critical growth exponent and the memory term satisfies the condition of exponent decay.