Abstract cauchy problems for quasi-linear evolution equations in the sense of hadamard

thispaper is devoted to the well-posedness of abstract cauchy problems for quasi-linear evolution equations. the notion of hadamard well-posedness is considered, and a new type of stability condition is introduced from the viewpoint of the theory of finite difference approximations. the result obtained here generalizes not only some results on abstract cauchy problems closely related with the theory of integrated semigroups or regularized semigroups but also the kato theorem on quasi-linear evolution equations. an application to some quasi-linear partial differential equation of weakly hyperbolic type is also given.

Digital Object Identifier:10.1112/S0024611503014643
Published with permission from the copyright holder. This is the institute's copy, as published in Proceedings of the London Mathematical Society, July 2004, Volume 89, Issue 1, Pages 123-160.
Publisher URL:http://dx.doi.org/10.1112/S0024611503014643
Copyright © 2004 London Mathematical Society. All rights reserved.