Evans, Lawrence C. Partial differential equations. 2nd ed. (English) Zbl 1194.35001 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) Cited in 5 ReviewsCited in 1006 Documents MathOverflow Questions: History of ODE and PDE reference request 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 Citations:Zbl 0902.35002 PDF BibTeX XML Cite \textit{L. C. Evans}, Partial differential equations. 2nd ed. Providence, RI: American Mathematical Society (AMS) (2010; Zbl 1194.35001) OpenURL