Convergence of hyperbolic approximations to higher-order PDEs for smooth solutions
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917314957410304 |
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| author | Giesselmann, Jan Ranocha, Hendrik |
| author_facet | Giesselmann, Jan Ranocha, Hendrik |
| contents | We prove the convergence of hyperbolic approximations for several classes of higher-order PDEs, including the Benjamin-Bona-Mahony, Korteweg-de Vries, Gardner, Kawahara, and Kuramoto-Sivashinsky equations, provided a smooth solution of the limiting problem exists. We only require weak (entropy) solutions of the hyperbolic approximations. Thereby, we provide a solid foundation for these approximations, which have been used in the literature without rigorous convergence analysis. We also present numerical results that support our theoretical findings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_04112 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Convergence of hyperbolic approximations to higher-order PDEs for smooth solutions Giesselmann, Jan Ranocha, Hendrik Numerical Analysis Analysis of PDEs 35L03, 35M11, 65M12, 65M06, 65M20 We prove the convergence of hyperbolic approximations for several classes of higher-order PDEs, including the Benjamin-Bona-Mahony, Korteweg-de Vries, Gardner, Kawahara, and Kuramoto-Sivashinsky equations, provided a smooth solution of the limiting problem exists. We only require weak (entropy) solutions of the hyperbolic approximations. Thereby, we provide a solid foundation for these approximations, which have been used in the literature without rigorous convergence analysis. We also present numerical results that support our theoretical findings. |
| title | Convergence of hyperbolic approximations to higher-order PDEs for smooth solutions |
| topic | Numerical Analysis Analysis of PDEs 35L03, 35M11, 65M12, 65M06, 65M20 |
| url | https://arxiv.org/abs/2508.04112 |