Premium
Stability of travelling waves for non‐convex scalar viscous conservation laws
Author(s) -
Jones Christopher K. R. T.,
Gardner Robert,
Kapitula Todd
Publication year - 1993
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/cpa.3160460404
Subject(s) - mathematics , semigroup , conservation law , traveling wave , resolvent , convexity , mathematical analysis , scalar (mathematics) , regular polygon , nonlinear system , stability (learning theory) , geometry , physics , quantum mechanics , machine learning , computer science , financial economics , economics
Travelling waves of a viscous conservation law (so‐called viscous profiles) are shown to be stable in polynomialy weighted L ∞ spaces. There is no assumption of convexity on the nonlinear term and thus earlier results of Il'in and Oleǐnik, Sattinger, and Kawashima and Matsumura are generalized. The method uses the semigroup of the linearized equation with solutions of the full problem expressed by the variation of constants formula. Estimates are derived for the semigroup through a new technique for estimating the resolvent. © 1993 John Wiley & Sons, Inc.