Nonlinear balance for reaction-diffusion equations under nonlinear boundary conditions: Dissipativity and blow-up

Abstract

The authors consider a reaction-diffusion equation in a bounded smooth domain Ω⊂R n with nonlinear flux terms on the boundary of Ω . They derive suitable conditions on the nonlinear terms of the problem which imply its dissipativity. The authors explore different situations in which there exist solutions of the problem that blow up in finite time. The main tools in the proof of the results are either energy estimates or sub- and super-solution techniques.