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Abstract:

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.

Registro:

Documento: Artículo
Título:The blow-up profile for a fast diffusion equation with a nonlinear boundary condition
Autor:Ferreira, R.; De Pablo, A.; Quiròs, F.; Rossi, J.D.
Filiación:Depto. De Matemàticas, U. Autònoma de Madrid, Madrid, 28049, Spain
Depto. De Matemàticas, U. Carlos III de Madrid, Leganés, 28911, Spain
Depto. De Matemàticas, U. Autònoma de Madrid, Madrid, 28049, Spain
Depto. De Matemàtica, F.C.E. Y N, UBA, Buenos Aires, 1428, Argentina
Palabras clave:Asymptotic behavior; Blow-up; Fast diffusion equation; Nonlinear boundary conditions
Año:2003
Volumen:33
Número:1
Página de inicio:123
Página de fin:146
DOI: http://dx.doi.org/10.1216/rmjm/1181069989
Título revista:Rocky Mountain Journal of Mathematics
Título revista abreviado:Rocky Mt. J. Math.
ISSN:00357596
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00357596_v33_n1_p123_Ferreira

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Citas:

---------- APA ----------
Ferreira, R., De Pablo, A., Quiròs, F. & Rossi, J.D. (2003) . The blow-up profile for a fast diffusion equation with a nonlinear boundary condition. Rocky Mountain Journal of Mathematics, 33(1), 123-146.
http://dx.doi.org/10.1216/rmjm/1181069989
---------- CHICAGO ----------
Ferreira, R., De Pablo, A., Quiròs, F., Rossi, J.D. "The blow-up profile for a fast diffusion equation with a nonlinear boundary condition" . Rocky Mountain Journal of Mathematics 33, no. 1 (2003) : 123-146.
http://dx.doi.org/10.1216/rmjm/1181069989
---------- MLA ----------
Ferreira, R., De Pablo, A., Quiròs, F., Rossi, J.D. "The blow-up profile for a fast diffusion equation with a nonlinear boundary condition" . Rocky Mountain Journal of Mathematics, vol. 33, no. 1, 2003, pp. 123-146.
http://dx.doi.org/10.1216/rmjm/1181069989
---------- VANCOUVER ----------
Ferreira, R., De Pablo, A., Quiròs, F., Rossi, J.D. The blow-up profile for a fast diffusion equation with a nonlinear boundary condition. Rocky Mt. J. Math. 2003;33(1):123-146.
http://dx.doi.org/10.1216/rmjm/1181069989