Ferreira de Pablo, Raúl and Pablo, Arturo de and Rossi, Julio D. (2007) Blow-up with logarithmic nonlinearities. Journal of Differential Equations, 240 (1). pp. 196-215. ISSN 0022-0396
We study the asymptotic behaviour of nonnegative solutions of the nonlinear diffusion equation in the half-line with a nonlinear boundary condition, ut = uxx − _(u + 1) logp(u + 1) (x, t) € R+ × (0, T),−ux(0, t) = (u + 1) logq(u + 1)(0, t) t € (0, T),u(x, 0) = u0(x) x € R+, with p, q, _ > 0. We describe in terms of p, q and 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.
|Uncontrolled Keywords:||Blow-up; Asymptotic behaviour; Nonlinear boundary conditions|
|Subjects:||Sciences > Mathematics > Differential equations|
|Deposited On:||05 Apr 2011 10:51|
|Last Modified:||05 Apr 2011 10:51|
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