New Trends in the Theory of Hyperbolic Equations (eBook, PDF)

Redaktion: Reissig, Michael; Schulze, Bert-Wolfgang

• Format: PDF

Produktbeschreibung

The present volume is dedicated to modern topics of the theory of hyperbolic equations such as evolution equations, multiple characteristics, propagation phenomena, global existence, influence of nonlinearities. It is addressed to beginners as well as specialists in these fields. The contributions are to a large extent self-contained. Key topics include: - low regularity solutions to the local Cauchy problem associated with wave maps; local well-posedness, non-uniqueness and ill-posedness results are proved - coupled systems of wave equations with different speeds of propagation; here pointwise decay estimates for solutions in spaces with hyperbolic weights come in - damped wave equations in exterior domains; the energy method is combined with the geometry of the exterior domain; for the critical part of the boundary a restricted localized effective dissipation is employed - the phenomenon of parametric resonance for wave map type equations; the influence of time-dependent oscillations on the existence of global small data solutions is studied - a unified approach to attack degenerate hyperbolic problems as weakly hyperbolic ones and Cauchy problems for strictly hyperbolic equations with non-Lipschitz coefficients - weakly hyperbolic Cauchy problems with finite time degeneracy; the precise loss of regularity depending on the spatial variables is determined; the main step is to find the correct class of pseudodifferential symbols and to establish a calculus which contains a symmetrizer.

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Produktdetails

• Verlag: Springer Basel
• Seitenzahl: 514
• Erscheinungstermin: 21. März 2006
• Englisch
• ISBN-13: 9783764373863
• Artikelnr.: 37398042

Autorenporträt

Bert-Wolfgang Schulze ist emeritierter Professor am Institut für Mathematik an der Universität Potsdam, Deutschland. Vor der politischen Wende war er Professor am Karl-Weierstrass-Institut in Berlin, 1984 Euler-Medaille der Akademie der Wisenschaften in Berlin. 1992-96 war er Leiter der Max-Planck-Arbeitsgruppe 'Partielle Differentialgleichungen und Komplexe Analysis' in Potsdam. Nach anfänglichem Studium in Geophysik erhielt er sein Universitätsdiplom in Mathematik in Leipzig 1968. Die Promotion zum Dr. rer.nat. 1970 und die Habilitation in Mathematik 1974 erfolgten an der Universität Rostock. Seine wissenschaftlichen Aktivitäten umfassen Potentialtheorie, Randwert-Probleme, pseudo-differentielle Algebren und Index-Theorie auf berandeten Mannigfaltgikeiten und Räumen mit Singularitäten, darunterTransmissions- und Riss Probleme, Asymptotik von Lösungen, Randwert-Theorie mit globalen Projektionsbedingungen.

Inhaltsangabe

From the contents:
Preface.- Wave Maps and Ill-posedness of their Cauchy Problem (P. D'Ancona and V. Georgiev).- On the Global Behaviour of Classical Solutions to Coupled Systems of Semilinear Wave Equations (H. Kubo and M. Ohta).- Decay and Global Existence for Nonlinear Wave Equations with Localized Dissipations in General Exterior Domains (M. Nakao).- Global Existence in the Cauchy Problem for Nonlinear Wave Equations with Variable Speed of Propagation (K. Yagdjian).- On the Nonlinear Cauchy Problem (M. Cicognani and L. Zanghirati).- Sharp Energy Estimates for a Class of Weakly Hyperbolic Operators (M. Dreher and I. Witt).