一类伪抛物型方程初边值问题

The Initial-boundary Problem of a Class of Pseudoparabolic Equations

本文讨论和一些重要的物理过程有着密切关系的一类伪抛物方程的初边值问题。首先利用强制不等式和连续性方法推广了现有的线性问题解的存在惟一性结果,然后利用Hilbert空间中Leray-Schauder度的同伦不变性,给出了一类非线性伪抛物方程解的存在性定理。

The study on the non-linear pseudoparabolic equation is currently very interesting because it arises in a variety of important physical processes. In this article, the initial-boundary problem of a class of pseudoparabolic equations is discussed. By using the continuity method and the coercivity inequality, the existence and uniqueness of the solution of the linear equation are obtained. Based on the invariance of the Leray-Schauder degree under homotopy transformation, the existence of the solution for the non-linear equation is also obtained.