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Title: Continuity of solutions of a quasilinear hyperbolic equation with hysteresis (English)
Author: Kordulová, Petra
Language: English
Journal: Applications of Mathematics
ISSN: 0862-7940 (print)
ISSN: 1572-9109 (online)
Volume: 57
Issue: 2
Year: 2012
Pages: 167-187
Summary lang: English
Category: math
Summary: This paper is devoted to the investigation of quasilinear hyperbolic equations of first order with convex and nonconvex hysteresis operator. It is shown that in the nonconvex case the equation, whose nonlinearity is caused by the hysteresis term, has properties analogous to the quasilinear hyperbolic equation of first order. Hysteresis is represented by a functional describing adsorption and desorption on the particles of the substance. An existence result is achieved by using an approximation of implicit time discretization scheme, a priori estimates and passage to the limit; in the convex case it implies the existence of a continuous solution. (English)
Keyword: hysteresis
Keyword: quasilinear hyperbolic equations
Keyword: generalized play operator
Keyword: discontinuous solution
MSC: 34C55
MSC: 35L04
MSC: 35L50
MSC: 35L60
MSC: 35L65
MSC: 35S30
idZBL: Zbl 1249.35214
idMR: MR2899730
DOI: 10.1007/s10492-012-0011-1
Date available: 2012-03-05T07:04:40Z
Last updated: 2020-07-02
Stable URL:
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