Singular convergence for semilinear wave equations with steep potential well
Analysis of PDEs
2026-02-20 v1
Abstract
We consider a semilinear wave equation in the whole space with a deep potential well. We prove that as the depth of the well tends to infinity, the solutions of the equation converge to the solutions of a wave equation defined on the bottom of the well, with Dirichlet condition on the boundary.
Cite
@article{arxiv.2602.17279,
title = {Singular convergence for semilinear wave equations with steep potential well},
author = {Martino Prizzi},
journal= {arXiv preprint arXiv:2602.17279},
year = {2026}
}
Comments
27 pages