Lectures on Nonlinear Hyperbolic Differential Equations (Mathématiques et Applications, 26) 1997th Edition by Lars Hörmander (PDF)

Description

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.

User’s Reviews

Editorial Reviews: From the Back Cover 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.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Hörmanders book in this subject is interesting, very interesting. Partly because it addresses nonlinear hyperbolic operators, and that is unusual. Almost any book in this subject would stay with the linear setting, and the hyperbolic non-linear notion is very tied to the field equations of Quantum Field Theory(QFT), which are usually hyperbolic and non-linear. A propagating wave after a boat follows a hyperbolic equation, and it is natural to ask what would have if we deform it to a non-linear hyperbolic problem. Much the same in QFT, where equations like the Dirac equation and the, of course non-linear, Yang-Mills equation are hyperbolic in Minkowski space-time or for that manner on any pseudo-Riemannian manifold of appropriate singnature.Now, physicists usually attack this via a holomorphic perspective on elliptic problems, where as many mathematicans would look at the relevant Cauchy problem, which may also be overdetermined or behave differently in different settings. There are very big differences between the elliptic and hyperbolic setting for non-linear operators(Indeed there are very large differences even in the linear setting.). The questions that arise are very delicate. And it is here that this book comes into play. Read it!

⭐Wonderfull Classic

⭐Poor paper quality, poor printing and poor binding. Mathematical content is of course absolutely great.Books published these days suffer from poor paper quality and poor binding !

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Free Download Lectures on Nonlinear Hyperbolic Differential Equations (Mathématiques et Applications, 26) 1997th Edition in PDF format
Lectures on Nonlinear Hyperbolic Differential Equations (Mathématiques et Applications, 26) 1997th Edition PDF Free Download
Download Lectures on Nonlinear Hyperbolic Differential Equations (Mathématiques et Applications, 26) 1997th Edition 1997 PDF Free
Lectures on Nonlinear Hyperbolic Differential Equations (Mathématiques et Applications, 26) 1997th Edition 1997 PDF Free Download
Download Lectures on Nonlinear Hyperbolic Differential Equations (Mathématiques et Applications, 26) 1997th Edition PDF
Free Download Ebook Lectures on Nonlinear Hyperbolic Differential Equations (Mathématiques et Applications, 26) 1997th Edition