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Convergence of hyperbolic approximations to higher-order PDEs for smooth solutions

  • 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.

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Metadaten
Author:Jan Giesselmann, Hendrik Ranocha
Document Type:Preprint
Language:English
Date of Publication (online):2025/08/06
Release Date:2026/01/06
Institutes:Technische Universität Darmstadt
Subprojects:C05
Licence (German):License LogoCreative Commons - CC BY-NC-ND - Namensnennung - Nicht kommerziell - Keine Bearbeitungen 4.0 International
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