Abstract:
We study positive solutions of a very fast diffusion equation, u t = (um-1ux)x, m < 0, in a bounded interval, 0 < x < L, with a quenching-type boundary condition at one end, u(0,t) = (T - t)1/(1-m) and a zero-flux boundary condition at the other, (um-1ux)(L,t) = 0. We prove that for m ≥ -1 regional quenching is not possible: the quenching set is either a single point or the whole interval. Conversely, if m < -1 single-point quenching is impossible, and quenching is either regional or global. For some lengths the above facts depend on the initial data. The results are obtained by studying the corresponding blow-up problem for the variable v = um-1. © 2005 The Royal Society of Edinburgh.
Registro:
Documento: |
Artículo
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Título: | On the quenching set for a fast diffusion equation: Regional quenching |
Autor: | Ferreira, R.; De Pablo, A.; Quirós, F.; Rossi, J.D. |
Filiación: | Departamento de Matemáticas, Universidad Carlos III de Madrid, Avda. de la Universidad 30, 28911 Leganés, Spain Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049 Madrid, Spain Departamento de Matemática, F.C.E y N., Universidad de Buenos Aires, 1428 Buenos Aires, Argentina
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Año: | 2005
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Volumen: | 135
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Número: | 3
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Página de inicio: | 585
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Página de fin: | 601
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Título revista: | Royal Society of Edinburgh - Proceedings A
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Título revista abreviado: | R. Soc. Edinburgh Proc. A
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ISSN: | 03082105
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Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03082105_v135_n3_p585_Ferreira |
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Citas:
---------- APA ----------
Ferreira, R., De Pablo, A., Quirós, F. & Rossi, J.D.
(2005)
. On the quenching set for a fast diffusion equation: Regional quenching. Royal Society of Edinburgh - Proceedings A, 135(3), 585-601.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03082105_v135_n3_p585_Ferreira [ ]
---------- CHICAGO ----------
Ferreira, R., De Pablo, A., Quirós, F., Rossi, J.D.
"On the quenching set for a fast diffusion equation: Regional quenching"
. Royal Society of Edinburgh - Proceedings A 135, no. 3
(2005) : 585-601.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03082105_v135_n3_p585_Ferreira [ ]
---------- MLA ----------
Ferreira, R., De Pablo, A., Quirós, F., Rossi, J.D.
"On the quenching set for a fast diffusion equation: Regional quenching"
. Royal Society of Edinburgh - Proceedings A, vol. 135, no. 3, 2005, pp. 585-601.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03082105_v135_n3_p585_Ferreira [ ]
---------- VANCOUVER ----------
Ferreira, R., De Pablo, A., Quirós, F., Rossi, J.D. On the quenching set for a fast diffusion equation: Regional quenching. R. Soc. Edinburgh Proc. A. 2005;135(3):585-601.
Available from: https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03082105_v135_n3_p585_Ferreira [ ]