Continuity of solutions of a quasilinear hyperbolic equation with hysteresis

Petra Kordulová

Applications of Mathematics (2012)

  • Volume: 57, Issue: 2, page 167-187
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Kordulová, Petra. "Continuity of solutions of a quasilinear hyperbolic equation with hysteresis." Applications of Mathematics 57.2 (2012): 167-187. <http://eudml.org/doc/246835>.

@article{Kordulová2012,
abstract = {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.},
author = {Kordulová, Petra},
journal = {Applications of Mathematics},
keywords = {hysteresis; quasilinear hyperbolic equations; generalized play operator; discontinuous solution; hysteresis; quasilinear hyperbolic equation; generalized play operator; discontinuous solution},
language = {eng},
number = {2},
pages = {167-187},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Continuity of solutions of a quasilinear hyperbolic equation with hysteresis},
url = {http://eudml.org/doc/246835},
volume = {57},
year = {2012},
}

TY - JOUR
AU - Kordulová, Petra
TI - Continuity of solutions of a quasilinear hyperbolic equation with hysteresis
JO - Applications of Mathematics
PY - 2012
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 57
IS - 2
SP - 167
EP - 187
AB - 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.
LA - eng
KW - hysteresis; quasilinear hyperbolic equations; generalized play operator; discontinuous solution; hysteresis; quasilinear hyperbolic equation; generalized play operator; discontinuous solution
UR - http://eudml.org/doc/246835
ER -

References

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