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Abstract:

We prove the existence of a nontrivially coupled parabolic system such that one of its components becomes unbounded at a finite time while the other remains bounded, a situation that we denote as non-simultaneous blow-up. Our system consists of two porous medium equations with coupled nonlinear flux boundary conditions. As a preliminary step, we will obtain a necessary and sufficient condition for blow-up. Next we characterize completely, in the case of increasing in time solutions, the set of parameters appearing in the system for which nonsimultaneous blow-up indeed occurs. In the course of our proofs we will obtain a necessary and sufficient condition for the blow-up of solutions to general porous medium type equations on the half-line with a prescribed flux at the boundary blowing up at a finite time, a result of independent interest.

Registro:

Documento: Artículo
Título:Non-simultaneous blow-up in a nonlinear parabolic system
Autor:Quirós, F.; Rossi, J.D.
Filiación:Departamento de Matemáticas, U. Autónoma de Madrid, 28049 Madrid, Spain
Departamento de Matemática, Universidad de Buenos Aires, Ciudad Universitaria, 1428 Buenos Aires, Argentina
Departamento de Matemática, Universidad Católica, Casilla 306, correo 22, Santiago, Chile
Palabras clave:Blow-up; Parabolic systems; Porous media
Año:2003
Volumen:3
Número:3
Página de inicio:397
Página de fin:418
Título revista:Advanced Nonlinear Studies
Título revista abreviado:Adv. Nonlinear Stud.
ISSN:15361365
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15361365_v3_n3_p397_Quiros

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Citas:

---------- APA ----------
Quirós, F. & Rossi, J.D. (2003) . Non-simultaneous blow-up in a nonlinear parabolic system. Advanced Nonlinear Studies, 3(3), 397-418.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15361365_v3_n3_p397_Quiros [ ]
---------- CHICAGO ----------
Quirós, F., Rossi, J.D. "Non-simultaneous blow-up in a nonlinear parabolic system" . Advanced Nonlinear Studies 3, no. 3 (2003) : 397-418.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15361365_v3_n3_p397_Quiros [ ]
---------- MLA ----------
Quirós, F., Rossi, J.D. "Non-simultaneous blow-up in a nonlinear parabolic system" . Advanced Nonlinear Studies, vol. 3, no. 3, 2003, pp. 397-418.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15361365_v3_n3_p397_Quiros [ ]
---------- VANCOUVER ----------
Quirós, F., Rossi, J.D. Non-simultaneous blow-up in a nonlinear parabolic system. Adv. Nonlinear Stud. 2003;3(3):397-418.
Available from: https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15361365_v3_n3_p397_Quiros [ ]