Boundary value problems for third-order pseudoelliptic equations with degeneration

  • Kozhanov Aleksandr I., kozhanov@math.nsc.ru Sobolev Institute of Mathematics, 4 Koptyug Avenue, Novosibirsk 630090, Russia; Novosibirsk State University, 1 Pirogov Street, Novosibirsk 630090, Russia
Keywords: third-order differential equation, degeneration, elliptic boundary value problem, regular solution, existence, uniqueness

Abstract

We study the solvability in Sobolev spaces of the Dirichlet problem and other elliptic problems for the differential equations

\begin{equation}

u_{tt}+\alpha(t)\frac{\partial}{\partial t}(\Delta u)+Bu=f(x,t)\tag{*}

\end{equation}

$x\in\Omega\subset\mathbb{R}^n,\,t\in(0,T),$ where $\Delta$ if the Laplace operator acting in the variables $x_1,\dots, x_n$ and $B$ is a second-order elliptic operator acting in the same variables $x_1,\dots, x_n$. A feature of the equations (∗) is that the sign of the function is not fixed in them. Existence and uniqueness theorems for regular solutions (having all generalized Sobolev’s derivatives in the equation) are proved for the problems under study.

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How to Cite
Kozhanov, A. (2020) “Boundary value problems for third-order pseudoelliptic equations with degeneration”, Mathematical notes of NEFU, 27(3), pp. 16-26. doi: https://doi.org/10.25587/SVFU.2020.63.12.002.
Section
Mathematics