The Klein-Gordon equation in a domain with time-dependent boundary
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To link to this article DOI: 10.1111/j.1467-9590.2008.00416.x
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.