Geodesic
Continuity of solutions of a quasilinear hyperbolic equation with hysteresis
Applications of Mathematics, Tome 57 (2012) no. 2, pp. 167-187.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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.
DOI : 10.1007/s10492-012-0011-1
Classification : 34C55, 35L04, 35L50, 35L60, 35L65, 35S30
Keywords: hysteresis; quasilinear hyperbolic equations; generalized play operator; discontinuous solution 
@article{10_1007_s10492_012_0011_1,
     author = {Kordulov\'a, Petra},
     title = {Continuity of solutions of a quasilinear hyperbolic equation with hysteresis},
     journal = {Applications of Mathematics},
     pages = {167--187},
     publisher = {mathdoc},
     volume = {57},
     number = {2},
     year = {2012},
     doi = {10.1007/s10492-012-0011-1},
     mrnumber = {2899730},
     zbl = {1249.35214},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10492-012-0011-1/}
}
TY  - JOUR
AU  - Kordulová, Petra
TI  - Continuity of solutions of a quasilinear hyperbolic equation with hysteresis
JO  - Applications of Mathematics
PY  - 2012
SP  - 167
EP  - 187
VL  - 57
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1007/s10492-012-0011-1/
DO  - 10.1007/s10492-012-0011-1
LA  - en
ID  - 10_1007_s10492_012_0011_1
ER  - 
%0 Journal Article
%A Kordulová, Petra
%T Continuity of solutions of a quasilinear hyperbolic equation with hysteresis
%J Applications of Mathematics
%D 2012
%P 167-187
%V 57
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1007/s10492-012-0011-1/
%R 10.1007/s10492-012-0011-1
%G en
%F 10_1007_s10492_012_0011_1
Kordulová, Petra. Continuity of solutions of a quasilinear hyperbolic equation with hysteresis. Applications of Mathematics, Tome 57 (2012) no. 2, pp. 167-187. doi : 10.1007/s10492-012-0011-1. http://geodesic.mathdoc.fr/articles/10.1007/s10492-012-0011-1/

Cité par Sources :