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Lectures on Nonlinear Hyperbolic Differential Equations : Math Matiques Et Applications - Lars Hormander

Lectures on Nonlinear Hyperbolic Differential Equations

Math Matiques Et Applications

Paperback Published: 17th July 1997
ISBN: 9783540629214
Number Of Pages: 290

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In this introductory textbook, a revised and extended version of well-known lectures by L. Hoermander 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.

Preface
Contents
Ordinary differential equations
Scalar first order equations with one space variable
Scalar first order equations with several variables
First order systems of conservation laws with one space
Compensated compactness
Nonlinear perturbations of the wave equation
Nonlinear perturbations of the Klein-Gordon equation
Microlocal analysis
Pseudo-differential operators of type 1,1
Paradifferential calculus
Propagation of singularities
Appendix on pseudo-Riemannian geometry
References
Index of notations
Index
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9783540629214
ISBN-10: 3540629211
Series: Math Matiques Et Applications
Audience: General
Format: Paperback
Language: English
Number Of Pages: 290
Published: 17th July 1997
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 24.18 x 16.56  x 1.85
Weight (kg): 0.5