The Klein–Gordon Equation in a Domain with Time-Dependent Boundary
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.
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Document Type: Research Article
Affiliations: University of Reading, UK
Publication date: October 1, 2008