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(1963)

Differential Equations and Their Applications

Continuity of solutions of a quasilinear hyperbolic equation with hysteresis

Petra Kordulová (2012)

Applications of Mathematics

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...

Continuity of the non-convex play operator in the space of rectifiable curves

Jana Kopfová, Vincenzo Recupero (2023)

Applications of Mathematics

We prove that the vector play operator with a uniformly prox-regular characteristic set of constraints is continuous with respect to the B V -norm and to the B V -strict metric in the space of rectifiable curves, i.e., in the space of continuous functions of bounded variation. We do not assume any further regularity of the characteristic set. We also prove that the non-convex play operator is rate independent.

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