Continuum limit of the discrete nonlinear Klein-Gordon equation
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Accesso online: | |
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| _version_ | 1866914687780651008 |
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| author | Chauleur, Quentin |
| author_facet | Chauleur, Quentin |
| contents | We study the convergence of solutions of the discrete nonlinear Klein-Gordon equation on an infinite lattice in the continuum limit, using recent tools developed in the context of nonlinear discrete dispersive equations. Our approach relies in particular on the use of bilinear estimates of the Shannon interpolation alongside controls on the growth of discrete Sobolev norms of the solution. We conclude by giving perspectives on uniform dispersive estimates for nonlinear waves on lattices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_13663 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Continuum limit of the discrete nonlinear Klein-Gordon equation Chauleur, Quentin Analysis of PDEs We study the convergence of solutions of the discrete nonlinear Klein-Gordon equation on an infinite lattice in the continuum limit, using recent tools developed in the context of nonlinear discrete dispersive equations. Our approach relies in particular on the use of bilinear estimates of the Shannon interpolation alongside controls on the growth of discrete Sobolev norms of the solution. We conclude by giving perspectives on uniform dispersive estimates for nonlinear waves on lattices. |
| title | Continuum limit of the discrete nonlinear Klein-Gordon equation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2402.13663 |