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arXiv · 2602.17279

Singular convergence for semilinear wave equations with steep potential well

Martino Prizzi
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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.

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Martino Prizzi. 2026-02-19. Singular convergence for semilinear wave equations with steep potential well. https://arxiv.org/abs/2602.17279

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