Blow-up for two nonlinear problems
The paper investigates the blow-up set of a first initial-boundary value problem for a multidimensional semilinear heat equation subject to some initial condition and a zero boundary condition. The blow-up of the \(L^q(\Omega)\)-norm for \(q\) large enough, and the complete blow-up were studied. The maximum principle and the parabolic version of Hopf's lemma for uniformly parabolic operator were used. A multidimensional Dirichlet problem for a semilinear Poisson equation subject to a zero boundary condition was also investigated.
scientific article; zbMATH DE number 1526181