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Boundedness of global solutions of a supercritical parabolic equation |
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| Authors: | Xinfu Chen Marek Fila Jong-Shenq Guo |
| Institution: | 1. Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, USA;2. Department of Applied Mathematics and Statistics, Comenius University, 842 48 Bratislava, Slovakia;3. Department of Mathematics, National Taiwan Normal University, 88, Sec. 4, Ting Chou Road, Taipei 116, Taiwan |
| Abstract: | We study radially symmetric classical solutions of the Dirichlet problem for a heat equation with a supercritical nonlinear source. We give a sufficient condition under which blow-up in infinite time cannot occur. This condition involves only the growth rate of the source term at infinity. We do not need the homogeneity property which played a key role in previous proofs of similar results. We also establish the blow-up rate for a class of solutions which blow up in finite time. |
| Keywords: | Global solutions Supercritical parabolic equation |
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