Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6417250 | Journal of Differential Equations | 2011 | 19 Pages |
Abstract
The aim of this paper is to present an approach for the study of well-posedness for diagonalizable hyperbolic systems of (pseudo)differential equations with characteristics which are not Lipschitz continuous with respect to both the time variable t (locally) and the space variables xâRn for |x|ââ. We introduce optimal conditions guaranteeing the well-posedness in the scale of the weighted Sobolev spaces Hs1,s2(Rn), cf. Introduction, with finite or arbitrarily small loss of regularity. We give explicit examples for ill-posedness of the Cauchy problem in the Schwartz spaces when the hypotheses on the growth for |x|ââ fail.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Marco Cappiello, Daniel Gourdin, Todor Gramchev,