Initial–Boundary Value Problem for a Nonlinear ModifiedBoussinesq Equation

We study the problem with a homogeneous Neumann boundary condition and classical initial conditions for a modified Boussinesq equation. Based on the compactness method, it is shown that the approximate analytical solution constructed in the form of Galerkin’s sum over the system of eigenfunctions of...

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Bibliographic Details
Published inDifferential equations Vol. 60; no. 8; pp. 1065 - 1073
Format Journal Article
LanguageEnglish
Published New York Springer Nature B.V 01.08.2024
Subjects
Boundary conditions
Boundary value problems
Boussinesq approximation
Convergence
Eigenvectors
Exact solutions
Initial conditions
Mathematical analysis
Neumann problem
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ISSN0012-2661
1608-3083
DOI10.1134/S001226612408007X

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Summary:We study the problem with a homogeneous Neumann boundary condition and classical initial conditions for a modified Boussinesq equation. Based on the compactness method, it is shown that the approximate analytical solution constructed in the form of Galerkin’s sum over the system of eigenfunctions of the Neumann boundary value problem converges -weakly to the exact solution.
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ISSN:0012-2661
1608-3083
DOI:10.1134/S001226612408007X