BOUNDARY VALUE PROBLEM FOR THE PSEUDOPARABOLIC EQUATIONS

Abstract

In the present paper the boundary value problem for the Sobolev type equation $$
\begin{cases}
\dfrac{\partial}{\partial t}L(u(t,x))+M(u(t,x))=f(t,x), \\ \qquad t>0,~~~x=(x_1,\ldots,x_n)\in \Omega\subset\mathbb{R}^n,\\
u\big|_{\partial\Omega}=0,\\
(Lu)(0,x)=g(z),\quad x\in\Omega,\end{cases}
$$

is considered, where L and M are second-order differential operators. It is proved that under some conditions this problem in the corresponding space has the unique solution.