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Convergence of the regularized short pulse equation to the short pulse one
Author(s) -
Coclite Giuseppe Maria,
Ruvo Lorenzo
Publication year - 2018
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201600301
Subject(s) - mathematics , compact space , a priori and a posteriori , pulse (music) , convergence (economics) , zero (linguistics) , nonlinear system , mathematical analysis , diffusion equation , dispersive partial differential equation , diffusion , differential equation , physics , philosophy , linguistics , economy , epistemology , service (business) , quantum mechanics , detector , optics , economics , thermodynamics , economic growth
Abstract We consider the regularized short‐pulse 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 solutions of the short‐pulse one. The proof relies on deriving suitable a priori estimates together with an application of the compensated compactness method in the L p setting.