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

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Rodríguez Bernal, Aníbal and Tajdine, Anas (2001) Nonlinear balance for reaction-diffusion equations under nonlinear boundary conditions: Dissipativity and blow-up. Journal of Differential Equations, 169 (2). pp. 332-372. ISSN 0022-0396

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Official URL: http://www.sciencedirect.com/science/article/pii/S0022039600939032


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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.


Item Type:Article
Uncontrolled Keywords:Energy estimates; Sub- and super-solution techniques; Heat-equations; Perturbation; Attractors
Subjects:Sciences > Mathematics > Functions
ID Code:19955
Deposited On:13 Feb 2013 16:30
Last Modified:12 Dec 2018 15:07

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