带扩散项的Cahn-Hilliard方程解的适定性

Well-posedness of Solution to Cahn-Hilliard Equation with Proliferation Term

研究有界域上一类带扩散项的广义Cahn-Hilliard方程解的适定性问题.此类方程主要用于描述物理和生物学中的一类扩散现象.在非线性扩散项满足更一般的假设条件下,利用标准的Galerkin方法和先验估计得到该方程在Neumann边界条件下弱解的适定性,并证明了解的相关正则性.

In this paper,the suitability problems of solutions for the generalized Cahn-Hilliard equation with proliferation term in the bounded domain are investigated.Such equations are mainly used to describe a class of diffusion phenomenas in physics and biology.In this paper,under the condition that the nonlinear diffusion term satisfies the more general assumptions,the well-posedness of the weak solution of the equation under the Neumann boundary condition is obtained by using the standard Galerkin scheme and a priori estimation,where the relevant regularity of the solution is proved.