Lectures on Nonlinear Hyperbolic Differential Equations (Mathématiques et Applications, 26, Band 26) - Softcover

Hörmander, Lars

 
9783540629214: Lectures on Nonlinear Hyperbolic Differential Equations (Mathématiques et Applications, 26, Band 26)
Softcover
ISBN 10: 3540629211 ISBN 13: 9783540629214
Verlag: Springer, 2009

Inhaltsangabe

In this introductory textbook, a revised and extended version of well-known lectures by L. Hörmander from 1986, four chapters are devoted to weak solutions of systems of conservation laws. Apart from that the book only studies classical solutions. Two chapters concern the existence of global solutions or estimates of the lifespan for solutions of nonlinear perturbations of the wave or Klein-Gordon equation with small initial data. Four chapters are devoted to microanalysis of the singularities of the solutions. This part assumes some familiarity with pseudodifferential operators which are standard in the theory of linear differential operators, but the extension to the more exotic classes of opertors needed in the nonlinear theory is presented in complete detail.

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Über die Autorin bzw. den Autor

Lars Hörmander was born on January 24, 1931, on the southern coast of Sweden. His secondary schooling, as well as his undergraduate and doctoral studies, took place in Lund, Sweden. His principal teacher and adviser at the University of Lund was Marcel Riesz, until his retirement, and then Lars Gårding. In 1956 he worked in the USA, at the universities of Chicago, Kansas, Minnesota and New York, before returning to a chair at the University of Stockholm. He remained a frequent visitor to the US, particularly to Stanford, and was Professor at the IAS, Princeton from 1964 to 1968. In 1968 he accepted a chair at the University of Lund, and remained there until his retirement in 1996. He passed away on November 25, 2012, in Lund, at the age of 81. Hörmander's life's work was devoted to the study of partial differential equations and its applications in complex analysis. In 1962 he was awarded the Fields Medal for his contributions to the general theory of linear partial differential operators. He was also awarded the Wolf Prize in 1988, and the Leroy P. Steele Prize in 2006. His Analysis of Linear Partial Differential Operators I-IV is considered a standard work on the subject of linear partial differential operators.

Von der hinteren Coverseite

This introduction to the theory of nonlinear hyperbolic differential equations, a revised and extended version of widely circulated lecture notes from 1986, starts from a very elementary level with standard existence and uniqueness theorems for ordinary differential equations, but they are at once supplemented with less well-known material, required later on. A detailed and explicit study of discontinuous solutions of a model equation, Burgers' equation, is then followed by a general study of solutions of conservation laws, with one unknown or one space variable. Asymptotic properties of solutions of the linear wave equation and the Klein-Gordon equation are studied in detail as a preparation for the study of solutions of nonlinear perturbations with small and smooth initial data. Existence of solutions for all times is proved for large space dimensions and lower bounds for the "lifespan" of the solutions are given in low space dimensions. The last four chapters are devoted to microlocal analysis of singularities of solutions of nonlinear differential equations by means of the paradifferential techniques of J.-M. Bony.

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Verlag
Springer
Erscheinungsdatum
2009
Sprache
Englisch
ISBN 10 
3540629211
ISBN 13 
9783540629214
Einband
Taschenbuch
Anzahl der Seiten
304
Kontakt zum Hersteller
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