Plasticity, ferromagnetism, ferroelectricity and other phenomena lead to quasilinear hyperbolic equations of the form where F is a (possibly discontinuous) hysteresis operator, and A is a second order elliptic operator. Existence of a solution is proved for an associated initial-and boundary-value
Asymptotic behaviour of a quasilinear hyperbolic equation with hysteresis
✍ Scribed by P. Kordulová
- Publisher
- Elsevier Science
- Year
- 2007
- Tongue
- English
- Weight
- 195 KB
- Volume
- 8
- Category
- Article
- ISSN
- 1468-1218
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We consider the asymptotic behavior of the solution of quasilinear hyperbolic equation with linear damping subsequent to [K. Nishihara, J. Differential Equations 131 (1996), 171 188]. In that article, the system with damping v t &u x =0, u t +p(v) x = &:u, p$(v)<0(v>0) was treated, and the converge
## Abstract This paper is concerned with the asymptotic behaviour of global classical solutions of diagonalizable quasilinear hyperbolic systems with linearly degenerate characteristic fields. Based on the existence results of global classical solutions, we prove that when __t__ tends to infinity,