一类带记忆项拟线性发展方程的适定性

On the Well-posedness of a Class of Quasilinear Evolution Equations with Memory Term

本文讨论无界域上带记忆项非经典扩散方程的适定性问题,其中非线性项满足任意阶多项式增长条件.我们运用非经典的Galerkin方法及分析技巧得到整体弱解的存在性,并证明解的唯一性和对初值的连续依赖性.

In this paper we discuss the well-posedness problem of a nonclassical diffusion equation over a unbounded domain with memory term and the nonlinearity term satisfying an arbitrary polynomial growth condition.The existence of the global weak solution is obtained by using the nonclassical Galerkin method and analytical techniques,and the uniqueness of the solution and the continuous dependence on initial values are showed.