Abstract Cauchy Problems for Quasi-Linear Evolution Equations in the Sense of Hadamard |
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Authors: | Tanaka Naoki |
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Institution: | Department of Mathematics, Faculty of Science, Okayama University Okayama 700-8530, Japan. E-mail: tanaka{at}math.okayama-u.ac.jp |
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Abstract: | This paper is devoted to the well-posedness of abstract Cauchyproblems for quasi-linear evolution equations. The notion ofHadamard well-posedness is considered, and a new type of stabilitycondition is introduced from the viewpoint of the theory offinite difference approximations. The result obtained here generalizesnot only some results on abstract Cauchy problems closely relatedwith the theory of integrated semigroups or regularized semigroupsbut also the Kato theorem on quasi-linear evolution equations.An application to some quasi-linear partial differential equationof weakly hyperbolic type is also given. 2000 Mathematics SubjectClassification 34G20, 47J25 (primary), 47D60, 47D62 (secondary). |
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Keywords: | abstract Cauchy problem in the sense of Hadamard regularized semigroup abstract quasi-linear evolution equation stability condition finite difference approximation |
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