一类变指标四阶退化抛物方程解的长时间行为和稳定性

Long-Time Behavior and Stability of Solutions for a Fourth-Order Degenerate Parabolic Equation with Variable Exponents

主要考虑了一类变指标四阶退化抛物方程问题,其存在性采用时间离散化技术,通过构造逼近解,结合能量估计获得一致性估计,进而得到存在性结果.在存在性基础上,利用熵泛函方法,得到解基于熵的能量估计,给出解的长时间行为,据此还获得解的稳定性.

A variable-exponent problem is mainly consider for a fourth-order degenerate parabolic equation.For the existence of the solutions,the semi-discrete technique and the energy estimates method are applied through the corresponding approximation solutions.On the basis of existence,an entropy functional is constructed,and the corresponding uniform estimates are obtained.Therefore,the long-time behavior is presented,and the stability is also obtained.