Lectures on Nonlinear Hyperbolic Differential Equations (Google eBook)

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Springer Science & Business Media, Jul 17, 1997 - Mathematics - 289 pages
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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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Scalar first order equations with one space variable
Scalar first order equations with several variables
First order systems of conservation laws with
Compensated compactness
Nonlinear perturbations of the wave equation
Nonlinear perturbations of the KleinGordon
Microlocal analysis
Pseudodifferential operators of type 11
Paradifferential calculus
Propagation of singularities
Appendix on pseudoRiemannian geometry

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About the author (1997)

Biography Lars HArmander

Born on January 24, 1931, on the southern coast of Sweden, Lars HArmander did his secondary schooling as well as his undergraduate and doctoral studies in Lund. His principle teacher and adviser at the University of Lund was Marcel Riesz until he returned, then Lars GA rding. 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, Sweden, where, today, he is Emeritus Professor.

HArmandera (TM)s lifetime work has been 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. His book Linear Partial Differential Operators published 1963 by Springer in the Grundlehren series was the first major account of this theory. Hid four volume text The Analysis of Linear Partial Differential Operators published in the same series 20 years later illustrates the vast expansion of the subject in that period.

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