Pohozaev, Stanislav The general blowup for nonlinear PDE’s. (English) Zbl 1064.35219 Haroske, Dorothee (ed.) et al., Function spaces, differential operators and nonlinear analysis. The Hans Triebel anniversary volume. Based on the lectures given at the international conference on function spaces, differential operators and nonlinear analysis, FSDONA-01, Teistungen, Germany, June 28–July 4, 2001, in honor of the 65th birthday of H. J. Triebel. Basel: Birkhäuser (ISBN 3-7643-6935-3/hbk). 141-159 (2003). The author presents some applications of the nonlinear capacity technique to nonexistence problems for nonlinear partial differential equations (PDE). The main goal of the author is to show that under suitable assumptions on the pair \((A,f)\), the sharp nonexistence theorem holds for the problem \[ A(u)\geq f(u),\quad x\in Q\subseteq \mathbb{R}^d, \qquad u\in S_{\text{loc}}(Q). \] The author considers some examples of nonlinear elliptic and parabolic types.For the entire collection see [Zbl 1011.00045]. Reviewer: Messoud A. Efendiev (Berlin) Cited in 3 Documents MSC: 35R45 Partial differential inequalities and systems of partial differential inequalities 35B40 Asymptotic behavior of solutions to PDEs 35J60 Nonlinear elliptic equations 35K55 Nonlinear parabolic equations Keywords:nonexistence problem; nonlinear capacity; nonlinear elliptic and parabolic PDE PDFBibTeX XMLCite \textit{S. Pohozaev}, in: Function spaces, differential operators and nonlinear analysis. The Hans Triebel anniversary volume. Based on the lectures given at the international conference on function spaces, differential operators and nonlinear analysis, FSDONA-01, Teistungen, Germany, June 28--July 4, 2001, in honor of the 65th birthday of H. J. Triebel. Basel: Birkhäuser. 141--159 (2003; Zbl 1064.35219)