Non-linear hyperbolic equations in domains with conical points : existence and regularity of solutions
著者
書誌事項
Non-linear hyperbolic equations in domains with conical points : existence and regularity of solutions
（Mathematical research = Mathematische Forschung, Bd. 84）
Akademie Verlag , VCH, c1995
1st ed
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注記
Includes bibliographical references
内容説明・目次
内容説明
In the first part of these notes, the existence of solutions to the corresponding linear equations is addressed, including the asymptotics of solutions near conical points. Using this information, the quasilinear equations are then solved by the standard iteration procedure. The exposition is based upon Kato's semigroup-theoretic approach for solving abstract linear hyperbolic equations and Schulze's theory of pseudo-differential operators on manifolds with conical singularities. The former method provides the general framework, whereas the latter is the basic tool in treating the specific difficulties of the non-smooth situation. Significantly, Schulze's theory admits a parameter-dependent version, which allows the description of the branching behaviour in time of discrete asymptotics of solutions near conical points. The calculus is presented in a form in which the operators are permitted to have symbols with limited smoothness, as arises in nonlinear problems. In an appendix, the applicability of energy methods is briefly discussed.
目次
- Hyperbolic partial differential equations
- pseudo-differential operators
- operators with non-smooth symbols
- operators on manifolds with conical singularities
- Kato's semigroup-theoretic approach for solving linear hyperbolic equations
- energy estimates
- branching behaviour of discrete asymptotics of solutions near conical points. (Part contents).
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