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I have good command in real and complex analysis as well i had studied ordinary differential equation. Now i am trying to study partial differential equation but facing a lot of problems. Please suggest me some books which are suitable for me. I start with Strauss book but it is not comfortable for me. Also tell me books in which Cauchy problem for PDE is given in very simple and nice form. I studied ODE from tenenbaum dover book which is very nice to digest. I want same type of books for PDE. Please suggest me . Thanks a lot.

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  • $\begingroup$ You might be interested by the discussions here. $\endgroup$
    – EditPiAf
    May 19, 2018 at 12:54
  • $\begingroup$ Thanks................ $\endgroup$
    – neelkanth
    May 19, 2018 at 13:17

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The book in PDE's people usually start with is Partial Differential Equations, by Lawrence C. Evans. You can find it here, for example.

This book covers the essentials you should start with when facing a first approach to PDE's. This is obviously subject to personal opinion. In particular you can find chapters on Representation formulas for both linear and non-linear equations, theory on Sobolev and Holder spaces, Elliptic equations, Calculus of Variations and much more. It is really a very complete book in my opinion.

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Lectures on partial differential equations by VI Arnold is a very well written book with nice geometric insight.

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Regards @neelkanth . You could try Introduction to Partial Differential Equations : A Computational Approach by Aslak Tveito and Ragnar Winther. It starts with Cauchy problem, method of characteristic, and it is quite soft. Besides proof, it also shows numerical simulation result. Thanks.

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If you need a bit of physics to keep the rigor interesting, I'd recommend Guenther and Lee's Partial Differential Equations of Mathematical Physics and Integral Equations. I used it in grad school, suited me fine. Looks like Dover publishes it now.

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You can try M.D.Raisinghania ordinary and partial differential equation book. A solved chapter on Cauchy problem is there in this book.

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  • $\begingroup$ Its very rough book..... $\endgroup$
    – neelkanth
    Sep 18, 2017 at 17:56

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