Michael Reissig / Bert-Wolfgang Schulze (eds.)

New Trends in the Theory of Hyperbolic Equations

Herausgegeben von Reissig, Michael; Schulze, Bert-Wolfgang

• Gebundenes Buch

Produktbeschreibung

Hyperbolic partial di?erential equations describe phenomena of material or wave transport in the applied sciences. Despite of considerable progress in the past decades,the mathematical theory still faces fundamental questions concerningthe in?uenceofnonlinearitiesormultiple characteristicsofthe hyperbolicoperatorsor geometric properties of the domain in which the evolution process is considered. The current volume is dedicated to modern topics of the theory of hyperbolic equations such as evolution equations multiple characteristics propagation phenomena global existence in?uence of nonlinearities. It is addressed both to specialists and to beginners in these ?elds. The c- tributions are to a large extent self-contained. The ?rst contribution is written by Piero D Ancona and Vladimir Georgiev. Piero D Ancona graduated in 1982 from Scuola Normale Superiore of Pisa. Since 1997he isfull professorat the Universityof Rome1. Vladimir Georgievgraduated in1981fromtheUniversityofSo?a.Since2000heisfullprofessorattheUniversity of Pisa. The ?rst part of the paper treats the existence of low regularity solutions to the local Cauchy problem associated with wave maps. This introductory part f- lows the classical approach developed by Bourgain, Klainerman, Machedon which yields local well-posedness results for supercritical regularity of the initial data. The nonuniqueness results are establishedbytheauthors under the assumption that the regularity of the initial data is subcritical. The approach is based on the use of self-similar solutions. The third part treats the ill-posedness results of the Cauchy problem for the critical Sobolev regularity. The approach is based on the e?ective application of the properties of a special family of solutions associated with geodesics on the target manifold.

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Produktdetails

• Operator Theory: Advances and Applications 159
• Verlag: Birkhäuser Basel / Springer, Basel
• Artikelnr. des Verlages: 11407928
• 2005
• Seitenzahl: 528
• Erscheinungstermin: 19. Juli 2005
• Englisch
• Abmessung: 250mm x 175mm x 34mm
• Gewicht: 1100g
• ISBN-13: 9783764372835
• ISBN-10: 3764372834
• Artikelnr.: 14718453

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).

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Wave Maps and Ill-posedness of their Cauchy Problem.- On the Global Behavior of Classical Solutions to Coupled Systems of Semilinear Wave Equations.- Decay and Global Existence for Nonlinear Wave Equations with Localized Dissipations in General Exterior Domains.- Global Existence in the Cauchy Problem for Nonlinear Wave Equations with Variable Speed of Propagation.- On the Nonlinear Cauchy Problem.- Sharp Energy Estimates for a Class of Weakly Hyperbolic Operators.