Investigation of the influence of parameters on the correctness of the conjugation problem for the Boussinesq~--- L\"ove

A. I. Kozhanov ; N. N. Shadrina

Čelâbinskij fiziko-matematičeskij žurnal, Tome 7 (2022) no. 1, pp. 30-42.

Résumé

The aim of this work is to study the solvability of boundary value problems for differential equations $u_{tt}-\Delta u_{tt}+\lambda\Delta u=\mu u+f(x,t)$ with the Dirichlet boundary conditions, as well as with some matching conditions on the line $t=0$. For the problems under study, the properties of existence, uniqueness and non-uniqueness of a regular solution are established (i.e. solutions having all generalized derivatives by S.L. Sobolev included in the equation).

Détail

Keywords: Boussinesq — Löve equation, boundary value problem, conjugation conditions, regular solution, existence of solution, uniqueness of solution, influence of parameters.

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