Abstract Cauchy problems for quasi-linear evolution equations in the sense of Hadamard
| Autor: | Naoki Tanaka |
|---|---|
| Rok vydání: | 2004 |
| Předmět: |
Cauchy problem
abstract quasi-linear evolution equation Pure mathematics Cauchy's convergence test Cauchy momentum equation General Mathematics Mathematical analysis Mathematics::Analysis of PDEs stability condition regularized semigroup finite difference approximation Elliptic partial differential equation abstract cauchy problem in the sense of hadamard Cauchy boundary condition Cauchy's integral theorem Hyperbolic partial differential equation Cauchy matrix Mathematics |
| Zdroj: | Proceedings of the London Mathematical Society. 89:123-160 |
| ISSN: | 1460-244X 0024-6115 |
| DOI: | 10.1112/s0024611503014643 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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