## Asymptotic behaviour of a quasilinear hyperbolic equation with hysteresis.(English)Zbl 1132.35312

Summary: The paper deals with the asymptotic behaviour of the solution of a quasilinear hyperbolic equation with hysteresis. A stability result for solution in $$L^{1}(\Omega )$$ is derived by the nonlinear semigroup approach.

### MSC:

 35B40 Asymptotic behavior of solutions to PDEs 35L60 First-order nonlinear hyperbolic equations 34C55 Hysteresis for ordinary differential equations 47J40 Equations with nonlinear hysteresis operators
Full Text:

### References:

 [1] Barbu, V., Nonlinear semigroups and differential equations in Banach spaces, (1976), Noordhoff International Publishing Leiden [2] Brokate, M.; Sprekels, J., Hysteresis and phase transitions, (1996), Springer Berlin · Zbl 0951.74002 [3] M.G. Crandall, An introduction to evolution governed by accretive operators in dynamical systems, Proceedings of the International Symposium, vol. I, Brown Univ. Providence, RI, 1974, Academic Press, New York, 1976, pp. 131-156. [4] Kopfová, J., Semigroup approach to the question of stability for a partial differential equation with hysteresis, J. math. anal. appl., 223, 272-287, (1998) · Zbl 0915.35014 [5] Pavel, M.H., Nonlinear evolution operators and semigroups, (1987), Springer Berlin [6] H.K. Rhee, R. Aris, N.R. Amundson, First order partial differential equations, Theory and Applications of Single Equations, vol. 1, Prentice-Hall, Englewood Cliffs, NJ, 1986. · Zbl 0699.35001 [7] Ruthen, D.M., Principles of adsorption and adsorption processes, (1984), Wiley New York [8] Showalter, R.E.; Peszynska, M., A transport model with adsorption hysteresis, Differential integ. equations, 11, 327-340, (1998) · Zbl 1004.35033 [9] Visintin, A., Differential models of hysteresis, (1995), Springer Berlin · Zbl 0656.73043 [10] P. Wittbold, Asymptotic behavior of certain nonlinear evolution equation in $$L^1$$, in: Progress in Partial Differential Equations: The Metz Surveys, vol. 2, 1992, pp. 216-230, Longman Sci. Tech., Harlow, 1993 (Pitman Res. Notes Math. Ser. vol. 296).
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.