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The Klein–Gordon Equation in a Domain with Time‐Dependent Boundary
Author(s) -
Pelloni B.,
Pinotsis D. A.
Publication year - 2008
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/j.1467-9590.2008.00416.x
Subject(s) - mathematics , boundary value problem , mathematical analysis , fourier transform , mixed boundary condition , nonlinear system , dirichlet boundary condition , integrable system , inversion (geology) , physics , quantum mechanics , paleontology , structural basin , biology
We solve a Dirichlet boundary value problem for the Klein–Gordon equation posed in a time‐dependent domain. Our approach is based on a general transform method for solving boundary value problems for linear and integrable nonlinear PDE in two variables. Our results consist of the inversion formula for a generalized Fourier transform, and of the application of this generalized transform to the solution of the boundary value problem.