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A product formula for semigroups of Lipschitz operators associated with abstract quasilinear evolution equations

✍ Scribed by Naoki Tanaka

Publisher
John Wiley and Sons
Year
2011
Tongue
English
Weight
244 KB
Volume
285
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

The notion of semigroups of Lipschitz operators associated with abstract quasilinear evolution equations is introduced and a product formula for such semigroups is established. The product formula obtained in the paper is applied to the solvability of the Cauchy problem for a first order quasilinear system through a finite difference scheme of the Lax‐Friedrichs type.

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## Abstract We use the method proposed by H. Kumano‐go in the classical case to construct a parametrix of the equation $ \textstyle {{\partial u} \over {\partial t}}$ + __q__ (__x, D__ )__u__ = 0 where __q__ (__x, D__ ) is a pseudo‐differential operator with symbol in the class introduced by W. Hoh