Partial differential equations. 2nd ed. (English) Zbl 1194.35001

Evans, Lawrence C.

Graduate Studies in Mathematics 19. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4974-3/hbk). xxi, 749 p. (2010).

This second edition of [Zbl 0902.35002] differs from the first one mainly by a new chapter 12 on nonlinear wave equations, by new Sections 4.1.2 on Turing instabilities, 4.3.2 on Radon transforms, 8.2.5 on local minimizers and 8.6.2 on Noether’s Theorem as well as by new exercises.
Chapter 12 concerns the initial value problem for semilinear wave equations \(u_{tt}-\Delta u= f(u)\) or for mildly quasilinear wave equations \(u_{tt}-\Delta u= f(Du,u_t, u)\). Results on local existence, critical power nonlinearities and blow-up are presented.

Reviewer: Lutz Recke (Berlin)

MSC:

35-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to partial differential equations
49-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to calculus of variations and optimal control

Keywords:

nonlinear wave equations; Radon transforms; Noether’s theorem