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Extinction of multiple shocks in the modular Burgers’ equation

Pelinovsky, Dmitry E. ; de Rijk, Björn 1
1 Institut für Analysis (IANA), Karlsruher Institut für Technologie (KIT)

Abstract:

We consider multiple shock waves in the Burgers’ equation with a modular advection term. It was previously shown that the modular Burgers’ equation admits a traveling viscous shock with a single interface, which is stable against smooth and exponentially localized perturbations. In contrast, we suggest in the present work with the help of energy estimates and numerical simulations that the evolution of shock waves with multiple interfaces leads to finite-time coalescence of two consecutive interfaces. We formulate a precise scaling law of the finite-time extinction supported by the interface equations and by numerical simulations


Volltext §
DOI: 10.5445/IR/1000151750
Veröffentlicht am 24.10.2022
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Analysis (IANA)
Publikationstyp Forschungsbericht/Preprint
Publikationsjahr 2022
Sprache Englisch
Identifikator ISSN: 0924-090X, 1573-269X
KITopen-ID: 1000151750
Vorab online veröffentlicht am 16.06.2022
Schlagwörter Analysis of PDEs, Dynamical Systems, Pattern Formation and Solitons
Nachgewiesen in Dimensions
arXiv
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