The Theory of Differential Equations (Universitext)


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Basic perturbation theory: Differential Equation, Regular Perturbation Part I

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Are you a frequent reader or book collector? Social responsibility Did you know that since , Biblio has used its profits to build 12 public libraries in rural villages of South America? A special order item has limited availability and the seller may source this title from another supplier. MathOverflow is a question and answer site for professional mathematicians. It only takes a minute to sign up. Most of the present books on pde analysis deal with the elliptic partial differential equations.

Is there some book related to rigorous analysis with hyperbolic pdes, and especially hyperbolic systems of pdes? I want to some great books on this subject for research. Thank you. It's funny that a similar question hasn't already appeared on MO. Other answers already give some good suggestions. Here's a bunch more. Note that the older ones may not be considered very pedagogical or rigorous by today's standards.

Hadamard, J. Courant, R. Methods of mathematical physics. II: Partial differential equations Interscience, ; German original Petrovsky, I. Leray, J. Hyperbolic differential equations Institute for Advanced Study, Princeton, A bunch more have appeared in more recent years, some of which have already been mentioned.

Here are a few other noteworthy ones.

Stochastic differential equations pdf

Dafermos, C. Klainerman, S. Lecture Notes in Analysis lecture notes, Princeton, Sorry for adverstising myself. But Sylvie Benzoni-Gavage and myself published in a rather complete monograph on the subject. In particular, we treat initial-boundary value problems, first linear and then nonlinear.

We apply the theory to the stability of multi-dimensional shock waves, in particular in gas dynamics. Multi-dimensional hyperbolic partial differential equations. First order systems and applications. One that comes to mind is A. It is surprisingly difficult to find expositions on first order hyperbolic systems of PDE's. There are two standard types: symmetric hyperbolic and strictly hyperbolic. Strictly hyperbolic systems were first studied by Lax, but the modern approach is to use pseudodifferential operators to obtain the energy estimates.

By now I can't remember where I learned this from. I suggest: S. Alinhac, Hyperbolic partial differential equations, Springer Universitext, The classic PDE book by F. John also gives a solid introduction to hyperbolic equations and systems, however his style of writing differs somewhat from todays. Sign up to join this community. The best answers are voted up and rise to the top.


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The Theory of Differential Equations (Universitext) The Theory of Differential Equations (Universitext)
The Theory of Differential Equations (Universitext) The Theory of Differential Equations (Universitext)
The Theory of Differential Equations (Universitext) The Theory of Differential Equations (Universitext)
The Theory of Differential Equations (Universitext) The Theory of Differential Equations (Universitext)
The Theory of Differential Equations (Universitext) The Theory of Differential Equations (Universitext)
The Theory of Differential Equations (Universitext) The Theory of Differential Equations (Universitext)
The Theory of Differential Equations (Universitext) The Theory of Differential Equations (Universitext)

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