Non–Linear Hyperbolic Equations in Domains with Conical Points: Existence and Regularity of Solutions: Vol 84 (Mathematical Research) - Softcover

Witt, Ingo

Softcover

ISBN 10: 3055016912 ISBN 13: 9783055016912

Publisher: Wiley VCH, 1995

Synopsis

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.

Edition details

• Publisher: Wiley VCH
• Publication date: 1995
• ISBN 10: 3055016912
• ISBN 13: 9783055016912
• Binding: Paperback
• Language: English
• Number of pages: 231