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

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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.
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 
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
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     journal = {Applications of Mathematics},
     pages = {167--187},
     year = {2012},
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     zbl = {1249.35214},
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