Blow-up with logarithmic nonlinearities
We study the asymptotic behaviour of nonnegative solutions of the nonlinear diffusion equation in the half-line with a nonlinear boundary condition,{Mathematical expression} with p, q, λ > 0. We describe in terms of p, q and λ when the solution is global in time and when it blows up in finite tim...
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2007
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00220396_v240_n1_p196_Ferreira http://hdl.handle.net/20.500.12110/paper_00220396_v240_n1_p196_Ferreira |
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| Sumario: | We study the asymptotic behaviour of nonnegative solutions of the nonlinear diffusion equation in the half-line with a nonlinear boundary condition,{Mathematical expression} with p, q, λ > 0. We describe in terms of p, q and λ when the solution is global in time and when it blows up in finite time. For blow-up solutions we find the blow-up rate and the blow-up set and we describe the asymptotic behaviour close to the blow-up time, showing that a phenomenon of asymptotic simplification takes place. We finally study the appearance of extinction in finite time. © 2007 Elsevier Inc. All rights reserved. |
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