Blow-up for a degenerate diffusion problem not in divergence form
We study the behaviour of solutions of the nonlinear diffusion equation in the half-line, ℝ+ = (0, ∞), with a nonlinear boundary condition, {ut = uuxx, (x, t) ∈ ℝ+ (0, T), -ux(0,t) = up(0,t), t ∈ (0,T), u(x,0) = u0(x), x ∈ ℝ+ with p > 0. We describe, in terms of p and the initial datum, when...
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2006
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00222518_v55_n3_p955_Ferreira http://hdl.handle.net/20.500.12110/paper_00222518_v55_n3_p955_Ferreira |
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paper:paper_00222518_v55_n3_p955_Ferreira2023-06-08T14:48:21Z Blow-up for a degenerate diffusion problem not in divergence form Asymptotic behaviour Blow-up Nonlinear boundary conditions We study the behaviour of solutions of the nonlinear diffusion equation in the half-line, ℝ+ = (0, ∞), with a nonlinear boundary condition, {ut = uuxx, (x, t) ∈ ℝ+ (0, T), -ux(0,t) = up(0,t), t ∈ (0,T), u(x,0) = u0(x), x ∈ ℝ+ with p > 0. We describe, in terms of p and the initial datum, when the solution is global in time and when it blows up in finite time. For blowing 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 in terms of a self-similar profile. The stationary character of the support is proved both for global solutions and blowing-up solutions. Also we obtain results for the problem in a bounded interval. Indiana University Mathematics Journal ©. 2006 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00222518_v55_n3_p955_Ferreira http://hdl.handle.net/20.500.12110/paper_00222518_v55_n3_p955_Ferreira |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Asymptotic behaviour Blow-up Nonlinear boundary conditions |
| spellingShingle |
Asymptotic behaviour Blow-up Nonlinear boundary conditions Blow-up for a degenerate diffusion problem not in divergence form |
| topic_facet |
Asymptotic behaviour Blow-up Nonlinear boundary conditions |
| description |
We study the behaviour of solutions of the nonlinear diffusion equation in the half-line, ℝ+ = (0, ∞), with a nonlinear boundary condition, {ut = uuxx, (x, t) ∈ ℝ+ (0, T), -ux(0,t) = up(0,t), t ∈ (0,T), u(x,0) = u0(x), x ∈ ℝ+ with p > 0. We describe, in terms of p and the initial datum, when the solution is global in time and when it blows up in finite time. For blowing 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 in terms of a self-similar profile. The stationary character of the support is proved both for global solutions and blowing-up solutions. Also we obtain results for the problem in a bounded interval. Indiana University Mathematics Journal ©. |
| title |
Blow-up for a degenerate diffusion problem not in divergence form |
| title_short |
Blow-up for a degenerate diffusion problem not in divergence form |
| title_full |
Blow-up for a degenerate diffusion problem not in divergence form |
| title_fullStr |
Blow-up for a degenerate diffusion problem not in divergence form |
| title_full_unstemmed |
Blow-up for a degenerate diffusion problem not in divergence form |
| title_sort |
blow-up for a degenerate diffusion problem not in divergence form |
| publishDate |
2006 |
| url |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00222518_v55_n3_p955_Ferreira http://hdl.handle.net/20.500.12110/paper_00222518_v55_n3_p955_Ferreira |
| _version_ |
1768545314298396672 |