Quasilinear first-order PDEs with hysteresis

[摘要] This paper deals with the Cauchy problem for a quasilinear first-order equation that includes a possibly discontinuous hysteresis operator F: partial derivative/partial derivative t[u + F(u)] + partial derivative u/partial derivative x = f in R, for t > 0. at ax Existence of a weak solution is proved for F equal to a completed relay operator. In the case of f 0, an entropy-type condition yields Lipschitz-continuous and monotone dependence on the initial data, hence uniqueness. (c) 2005 Elsevier Inc. All rights reserved.

[发布日期] 2005-12-15

[关键词] hysteresis;hyperbolic equations;weak formulation;entropy condition