The blow-up profile for a fast diffusion equation with a nonlinear boundary condition
We study positive solutions of a fast diffusion equation in the half-line with a nonlinear boundary condition, (ut=(um xx (x, t)∈'R+×(0, T), (-um)x(0, t) = up(0, t)t∈(0, T), u(x, 0)=u0(x) x∈R+, where 0<m<1 and p>0 are parameters. We describe in terms of p and m when all sol...
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2003
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00357596_v33_n1_p123_Ferreira http://hdl.handle.net/20.500.12110/paper_00357596_v33_n1_p123_Ferreira |
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paper:paper_00357596_v33_n1_p123_Ferreira2023-06-08T15:01:15Z The blow-up profile for a fast diffusion equation with a nonlinear boundary condition Asymptotic behavior Blow-up Fast diffusion equation Nonlinear boundary conditions We study positive solutions of a fast diffusion equation in the half-line with a nonlinear boundary condition, (ut=(um xx (x, t)∈'R+×(0, T), (-um)x(0, t) = up(0, t)t∈(0, T), u(x, 0)=u0(x) x∈R+, where 0<m<1 and p>0 are parameters. We describe in terms of p and m when all solutions exist globally in time, when all solutions blow up in a finite time, and when there are both blowing up and global solutions. For blowing up solutions we find the blow-up rate and the blow-up set and we describe the asymptotic behavior close to the blow-up time T in terms of a self-similar profile. © 2003 Rocky Mountain Mathematics Consortium. 2003 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00357596_v33_n1_p123_Ferreira http://hdl.handle.net/20.500.12110/paper_00357596_v33_n1_p123_Ferreira |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
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R-134 |
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Asymptotic behavior Blow-up Fast diffusion equation Nonlinear boundary conditions |
| spellingShingle |
Asymptotic behavior Blow-up Fast diffusion equation Nonlinear boundary conditions The blow-up profile for a fast diffusion equation with a nonlinear boundary condition |
| topic_facet |
Asymptotic behavior Blow-up Fast diffusion equation Nonlinear boundary conditions |
| description |
We study positive solutions of a fast diffusion equation in the half-line with a nonlinear boundary condition, (ut=(um xx (x, t)∈'R+×(0, T), (-um)x(0, t) = up(0, t)t∈(0, T), u(x, 0)=u0(x) x∈R+, where 0<m<1 and p>0 are parameters. We describe in terms of p and m when all solutions exist globally in time, when all solutions blow up in a finite time, and when there are both blowing up and global solutions. For blowing up solutions we find the blow-up rate and the blow-up set and we describe the asymptotic behavior close to the blow-up time T in terms of a self-similar profile. © 2003 Rocky Mountain Mathematics Consortium. |
| title |
The blow-up profile for a fast diffusion equation with a nonlinear boundary condition |
| title_short |
The blow-up profile for a fast diffusion equation with a nonlinear boundary condition |
| title_full |
The blow-up profile for a fast diffusion equation with a nonlinear boundary condition |
| title_fullStr |
The blow-up profile for a fast diffusion equation with a nonlinear boundary condition |
| title_full_unstemmed |
The blow-up profile for a fast diffusion equation with a nonlinear boundary condition |
| title_sort |
blow-up profile for a fast diffusion equation with a nonlinear boundary condition |
| publishDate |
2003 |
| url |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00357596_v33_n1_p123_Ferreira http://hdl.handle.net/20.500.12110/paper_00357596_v33_n1_p123_Ferreira |
| _version_ |
1768546245171740672 |