A singular limit problem for the Kudryashov-Sinelshchikov equation

2014/11/18 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 #Nonlinear Photonic Systems #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1411.5033

openalex publication_date 2014/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the Kudryashov-Sinelshchikov equation, which contains nonlinear dispersive effects. We prove that as the diffusion parameter tends to zero, the solutions of the dispersive equation coverge to the entropy ones of the Burgers equation. The proof relies on deriving suitable a priori estimates together with an application of the compansated compactness method in the L^p setting.

Related

• A singular limit problem for conservation laws related to the Rosenau-Korteweg-de Vries equation
• A singular limit problem for conservation laws related to the Rosenau equation
• Convergence of the Ostrovsky equation to the Ostrovsky-Hunter one
• A singular limit problem for the Rosenau-Korteweg-de Vries-regulared long wave and Rosenau-korteweg-de Viers equation
• A singular limit problem for the Ibragimov-Shabat equation