We study certain boundary value problems for the one-dimensional wave equation posed in a time-dependent domain. The approach we propose is based on a general transform method for solving boundary value problems for integrable nonlinear PDE in two variables, that has been applied extensively to the study of linear parabolic and elliptic equations. Here we analyse the wave equation as a simple illustrative example to discuss the particular features of this method in the context of linear hyperbolic PDEs, which have not been studied before in this framework.
- Boundary value problems
- Riemann–Hilbert problems
- Moving boundary
- Wave equation
Pelloni, B., & Pinotsis, D. (2010). Moving boundary value problems for the wave equation. Journal of Computational and Applied Mathematics, 234(6), 1685-1691. https://doi.org/10.1016/j.cam.2009.08.016