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Effects of a saturating dissipation in Burgers‐type equations
Author(s) -
Kurganov A.,
Rosenau P.
Publication year - 1997
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/(sici)1097-0312(199708)50:8<753::aid-cpa2>3.0.co;2-5
Subject(s) - mathematics , dissipation , smoothness , burgers' equation , jump , initial value problem , type (biology) , mathematical analysis , partial differential equation , physics , thermodynamics , ecology , biology , quantum mechanics
We propose and study a new variant of the Burgers equation with dissipation fluxes that saturate as the gradients become unbounded. If the upstream‐downstream transition is above a critical threshold, the corresponding Riemann problem admits a weak solution wherein part of the transit is accomplished by a jump. It is shown that the solution to a Cauchy problem with sufficiently small compact or periodic initial data preserves its initial smoothness. © 1997 John Wiley & Sons, Inc.