Lectures on Partial Differential Equations (Universitext)

Vladimir Arnold
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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.

Partial Differential Equations - Giovanni Bellettini - Lecture 01

Here are a few other noteworthy ones. 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.

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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.

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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. Japan Carlos E.

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Solonnikov , and N. MR Finite amplitude side-band stability of a viscous film. Local and global analysis.

Numerical solutions of the Korteweg-de Vries equation and its generalizations by the split-step Fourier method. In: A. Newell, editor Nonlinear Wave Motion , Amer. Long waves on liquid films.

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On the Benney-Lin and Kawahara equations. MR 98e 4. The initial-value problem for the Korteweg-de Vries equation. A MR 5. Hairer, S.

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Solving Ordinary Differential Equations I. Nonstiff Problems.

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Second edition. Springer, Berlin, MR 94c 6. Karlsen, K. Lie, and N.

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Arnold, Lectures on Partial Differential Equations. Lectures on Partial Differential Equations Universitext. Vladimir Arnold. He had very strong opinions on how this approach—which was most popularly implemented by the Bourbaki school in France—initially had a negative impact on French mathematical education , and then later on that of other countries as well. Gromov , S. Basel etc.

European Math. MR j 7.

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Karlsen, and N. Operator splitting methods for generalized Korteweg-de Vries equations. Courant, R. Methods of mathematical physics.

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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. 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.

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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.