Boundary value problem for the pseudoparabolic equations

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