Article ID Journal Published Year Pages File Type
4613563 Journal of Differential Equations 2006 23 Pages PDF
Abstract

We consider the Cauchy problem for linear and quasilinear symmetrizable hyperbolic systems with coefficients depending on time and space, not smooth in t and growing at infinity with respect to x. We discuss well-posedness in weighted Sobolev spaces, showing that the non-Lipschitz regularity in t has an influence not only on the loss of derivatives of the solution but also on its behaviour for |x|→∞. We provide examples to prove that the latter phenomenon cannot be avoided.

Related Topics
Physical Sciences and Engineering Mathematics Analysis