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A singular limit problem for the Kudryashov‐Sinelshchikov equation
Author(s) -
Coclite Giuseppe Maria,
di Ruvo Lorenzo
Publication year - 2017
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201500146
Subject(s) - compact space , burgers' equation , mathematics , a priori and a posteriori , limit (mathematics) , nonlinear system , zero (linguistics) , entropy (arrow of time) , continuation , mathematical analysis , computer science , physics , partial differential equation , thermodynamics , philosophy , linguistics , epistemology , quantum mechanics , programming language
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 converge to the entropy ones 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.