A singular limit problem for conservation laws related to the Rosenau equation

2015/03/12 by Giuseppe Maria Coclite, Coclite, G. M., Lorenzo di Ruvo +1
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Fractional Differential Equations Solutions #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1503.07400

openalex publication_date 2015/03/12 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

We consider the Rosenau equation, which contains nonlinear dispersive effects. We prove that as the diffusion parameter tends to zero, the solutions of the dispersive equation converge to discontinuous weak solution of the Burgers equation. The proof relies on deriving suitable a priori estimates together with an application of the compensated compactness method in the L^p setting.

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