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arXiv · 2508.04112

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

Jan Giesselmann·Hendrik Ranocha
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Abstract

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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Jan Giesselmann, Hendrik Ranocha. 2025-08-06. Convergence of hyperbolic approximations to higher-order PDEs for smooth solutions. https://doi.org/10.5802/jcm.144

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