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Abstract:

We study nonnegative solutions of {ut = (um)xx, (x,t)ε(0,L) × (0,T), {-(um)x(0,t) = up(0,t), tε(0,T), {(u,m)x(L,t) = -λuq(L,t), tε(0,T), {u(x,0) = u0(x), xε(0,L), where m, p, q, λ and L are positive parameters. For different values of the parameters three situations may occur: (1) all solutions of this problem exist for all t > 0; (2) for certain initial data functions the solution exists for all t > 0 while for others the solution blows up as t ↗ T for some finite T; (3) excepting the trivial solution when u0 ≡ 0, all solutions blow up as t ↗ T for some finite T. We identify in terms of the parameters which of them actually happens. For solutions which blow up we find the blow-up rate and the blow-up set. © 2002 Elsevier Science (USA).

Registro:

Documento: Artículo
Título:The balance between nonlinear inwards and outwards boundary flux for a nonlinear heat equation
Autor:Ferreira, R.; Quirós, F.; Rossi, J.D.
Filiación:Departamento De Matemáticas, U. Autónoma De Madrid, Madrid, 28049, Spain
Departamento De Matemática, F.C.E Y N., UBA, (1428) Buenos Aires, Argentina
Año:2002
Volumen:184
Número:1
Página de inicio:259
Página de fin:282
DOI: http://dx.doi.org/10.1006/jdeq.2001.4147
Título revista:Journal of Differential Equations
Título revista abreviado:J. Differ. Equ.
ISSN:00220396
CODEN:JDEQA
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00220396_v184_n1_p259_Ferreira

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Citas:

---------- APA ----------
Ferreira, R., Quirós, F. & Rossi, J.D. (2002) . The balance between nonlinear inwards and outwards boundary flux for a nonlinear heat equation. Journal of Differential Equations, 184(1), 259-282.
http://dx.doi.org/10.1006/jdeq.2001.4147
---------- CHICAGO ----------
Ferreira, R., Quirós, F., Rossi, J.D. "The balance between nonlinear inwards and outwards boundary flux for a nonlinear heat equation" . Journal of Differential Equations 184, no. 1 (2002) : 259-282.
http://dx.doi.org/10.1006/jdeq.2001.4147
---------- MLA ----------
Ferreira, R., Quirós, F., Rossi, J.D. "The balance between nonlinear inwards and outwards boundary flux for a nonlinear heat equation" . Journal of Differential Equations, vol. 184, no. 1, 2002, pp. 259-282.
http://dx.doi.org/10.1006/jdeq.2001.4147
---------- VANCOUVER ----------
Ferreira, R., Quirós, F., Rossi, J.D. The balance between nonlinear inwards and outwards boundary flux for a nonlinear heat equation. J. Differ. Equ. 2002;184(1):259-282.
http://dx.doi.org/10.1006/jdeq.2001.4147