BOUNDARY VALUE PROBLEM FOR THE PSEUDOPARABOLIC EQUATIONS - Ghorbanian, Siavash (Proceedings of the YSU A: Physical and Mathematical Sciences, 2010)
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.
Keywords: Sobolev type equations; pseudoparabolic equations; monotone and radial operators