Mueller, Carl E.; Weissler, Fred B. Single point blow-up for a general semilinear heat equation. (English) Zbl 0597.35057 Indiana Univ. Math. J. 34, 881-913 (1985). This paper is concerned with the behaviour of solutions to the semilinear heat equation which is formally equivalent to the integral equation \[ u(t)=e^{tQ}f+\int^{t}_{0}e^{(t-s)Q} F(u(s))ds, \] where \(Q=\Delta -\lambda I\), \(e^{tQ}=e^{-t\lambda} e^{t\Delta}\) and \(e^{t\Delta}\) is the heat semigroup with homogeneous Dirichlet boundary conditions on \(\Omega\). The main result of this paper is that, under certain conditions, solutions of this equation which blow up in finite time in fact blow up only at a single point. Reviewer: V.Mustonen Cited in 1 ReviewCited in 31 Documents MSC: 35K05 Heat equation 47D03 Groups and semigroups of linear operators 35B65 Smoothness and regularity of solutions to PDEs 45G10 Other nonlinear integral equations Keywords:blow up of solutions; semilinear heat equation; heat semigroup PDFBibTeX XMLCite \textit{C. E. Mueller} and \textit{F. B. Weissler}, Indiana Univ. Math. J. 34, 881--913 (1985; Zbl 0597.35057) Full Text: DOI