一类半线性伪抛物方程的初边值问题

The Initial Boundary Value Problem for a Class of Semilinear Pseudo-Parabolic Equations

研究一类退化的半线性伪抛物方程的初边值问题.借助势井理论,利用Galerkin方法、Aubin紧性定理及单调算子的理论,得到弱解的整体存在性与爆破方面的结论,并研究解具有真空隔离现象.

In this paper, the initial boundary value problem of a class of degenerate semilinear pseudo-parabolic equations is considered. With the help of the potential well, the Galerkin method, the Aubin compactness theorem and the monotonic operator theory, the global existence and uniqueness of the weak solution are obtained, where the vacuum isolation phenomenon is studied. Furthermore, the blow-up result for some suitable initial data is given.