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Abstract:

We study the possibility of defining a nontrivial continuation after the blow-up time for a system of two heat equations with a nonlinear coupling at the boundary. It turns out that any possible continuation that verifies a maximum principle is identically infinity everywhere after the blow-up time; that is, both components blow up completely. We also analyze the propagation of the singularity to the whole space, the avalanche, when blow-up is non-simultaneous.

Registro:

Documento: Artículo
Título:Complete BLOW-UP AND AVALANCHE FORMATION FOR A PARABOLIC SYSTEM WITH NON-SIMULTANEOUS BLOW-Up
Autor:Brandie, C.; Quirós, F.; Rossi, J.D.
Filiación:Departamento de Matemáticas, U. Carlos III de Madrid, 28911 Leganés, Spain
Departamento de Matemáticas, U. Autónoma de Madrid, 28049 Madrid, Spain
Departamento de Matemática FCEyN, U. de Buenos Aires, 1428 Buenos Aires, Argentina
Palabras clave:Avalanche; Complete blow-up; Nonlinear boundary conditions; Parabolic system
Año:2010
Volumen:10
Número:3
Página de inicio:659
Página de fin:679
Título revista:Advanced Nonlinear Studies
Título revista abreviado:Adv. Nonlinear Stud.
ISSN:15361365
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15361365_v10_n3_p659_Brandie

Referencias:

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  • Galaktionov, V.A., Vázquez, J.L., The problem ofblow-up in nonlinear parabolic equations (2002) Current Developments in Partial Differential Equations (Temuco, 1999 Discrete, 8 (2), pp. 399-433. , Discrete Contin. Dyn. Syst
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Citas:

---------- APA ----------
Brandie, C., Quirós, F. & Rossi, J.D. (2010) . Complete BLOW-UP AND AVALANCHE FORMATION FOR A PARABOLIC SYSTEM WITH NON-SIMULTANEOUS BLOW-Up. Advanced Nonlinear Studies, 10(3), 659-679.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15361365_v10_n3_p659_Brandie [ ]
---------- CHICAGO ----------
Brandie, C., Quirós, F., Rossi, J.D. "Complete BLOW-UP AND AVALANCHE FORMATION FOR A PARABOLIC SYSTEM WITH NON-SIMULTANEOUS BLOW-Up" . Advanced Nonlinear Studies 10, no. 3 (2010) : 659-679.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15361365_v10_n3_p659_Brandie [ ]
---------- MLA ----------
Brandie, C., Quirós, F., Rossi, J.D. "Complete BLOW-UP AND AVALANCHE FORMATION FOR A PARABOLIC SYSTEM WITH NON-SIMULTANEOUS BLOW-Up" . Advanced Nonlinear Studies, vol. 10, no. 3, 2010, pp. 659-679.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15361365_v10_n3_p659_Brandie [ ]
---------- VANCOUVER ----------
Brandie, C., Quirós, F., Rossi, J.D. Complete BLOW-UP AND AVALANCHE FORMATION FOR A PARABOLIC SYSTEM WITH NON-SIMULTANEOUS BLOW-Up. Adv. Nonlinear Stud. 2010;10(3):659-679.
Available from: https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15361365_v10_n3_p659_Brandie [ ]