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- W2236632160 abstract "where w = F(u) represents hysteresis. It is well known that even for φ and u0 smooth (1.1) exhibits singularities in a finite time. To be able to continue the solution, one has to pass to a generalized concept of weak solutions where discontinuities are allowed. Weak solutions are in general not uniquely determined by the data, and further physically motivated conditions have to be prescribed. The simplest one is an entropy condition stating that the entropy of the system must be decreasing, generalized by Olejnik [5]. A different condition was derived by Kružkov [4] and there are many others. Inspired by Kružkov’s work, Crandall [1] shows that the unique integral solution of (1.1), constructed by the method of nonlinear semigroups, satisfies an entropy condition derived by Kružkov. In the first section we give a brief overview of their results. We consider Equation (1.2) coupled with a generalized play or PrandtlIshlinskii operator of play type. It was expected (see [9]) that the integral" @default.
- W2236632160 created "2016-06-24" @default.
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- W2236632160 date "2005-01-01" @default.
- W2236632160 modified "2023-10-14" @default.
- W2236632160 title "Entropy condition for a quasilinear hyperbolic equation with hysteresis" @default.
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- W2236632160 doi "https://doi.org/10.57262/die/1356060197" @default.
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