Blow Up for Reaction Diffusion Equations Under Dynamical Boundary Conditions

• Published in: Communications in partial differential equations Vol. 28; no. 1-2; pp. 223 - 247
• Main Authors: von Below, Joachim, Pincet Mailly, Gaëlle
• Format: Journal Article
• Language: English
• Published: Taylor & Francis Group 06.01.2003; Taylor & Francis
• Subjects: AMS Subject Classification 2000; Blow up; Dynamical boundary conditions; Mathematics; Nonlinear parabolic problems; blow up; Nonlinear parabolic problems; dynamical boundary conditions
• ISSN: 0360-5302; 1532-4133
• DOI: 10.1081/PDE-120019380

For a class of reaction diffusion equations in a bounded domain under dissipative dynamical time lateral boundary conditions, the occurence of blow up phenomena is shown by comparison of solutions, as well as by energy and spectral methods. Moreover, the dependence of the blow up time on different boundary conditions is investigated, where the dynamical boundary condition interpolates between the Neumann boundary condition and a certain Dirichlet boundary condition related to the initial condition. Some of the techniques presented here apply also to certain parabolic equations with degenerate principal part. † Dedicated to Professor Helmut Kaul on the occasion of his 65th birthday.