Artículo

De Pablo, A.; Quirós, F.; Rossi, J.D. "Asymptotic simplification for a reaction-diffusion problem with a nonlinear boundary condition" (2002) IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications). 67(1):69-98
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Abstract:

We study non-negative solutions of the porous medium equation with a source and a nonlinear flux boundary condition, ut = (um)xx + up in (0, ∞) × (0, T); -(um)x (0, t) = uq(0, t) for t ∈ (0, T); u(x, 0) = u0(x) in (0, ∞), where m > 1, p, q > 0 are parameters. For every fixed m we prove that there are two critical curves in the (p, q)-plane: (i) the critical existence curve, separating the region where every solution is global from the region where there exist blowing-up solutions, and (ii) the Fujita curve, separating a region of parameters in which all solutions blow up from a region where both global in time solutions and blowing-up solutions exist. In the case of blow up we find the blow-up rates, the blow-up sets and the blow-up profiles, showing that there is a phenomenon of asymptotic simplification. If 2q < p + m the asymptotics are governed by the source term. On the other hand, if 2q > p + m the evolution close to blow up is ruled by the boundary flux. If 2q = p + m both terms are of the same order.

Registro:

Documento: Artículo
Título:Asymptotic simplification for a reaction-diffusion problem with a nonlinear boundary condition
Autor:De Pablo, A.; Quirós, F.; Rossi, J.D.
Filiación:Departamento de Matemáticas, Universidad Carlos III de Madrid, 28911 Leganés, Spain
Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049 Madrid, Spain
Departamento de Matemática, FCE y N, UBA, (1428) Buenos Aires, Argentina
Palabras clave:Blow up; Nonlinear boundary condition; Porous medium equation; Boundary conditions; Boundary value problems; Curve fitting; Integration; Mathematical models; Porous materials; Theorem proving; Thermal conductivity; Asymptotic simplification; Blow up solution; Fujita curve; Nonlinear boundary condition; Porous medium equation; Reaction diffusion problem; Asymptotic stability
Año:2002
Volumen:67
Número:1
Página de inicio:69
Página de fin:98
DOI: http://dx.doi.org/10.1093/imamat/67.1.69
Título revista:IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)
Título revista abreviado:IMA J Appl Math
ISSN:02724960
CODEN:IJAMD
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02724960_v67_n1_p69_DePablo

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Citas:

---------- APA ----------
De Pablo, A., Quirós, F. & Rossi, J.D. (2002) . Asymptotic simplification for a reaction-diffusion problem with a nonlinear boundary condition. IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications), 67(1), 69-98.
http://dx.doi.org/10.1093/imamat/67.1.69
---------- CHICAGO ----------
De Pablo, A., Quirós, F., Rossi, J.D. "Asymptotic simplification for a reaction-diffusion problem with a nonlinear boundary condition" . IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications) 67, no. 1 (2002) : 69-98.
http://dx.doi.org/10.1093/imamat/67.1.69
---------- MLA ----------
De Pablo, A., Quirós, F., Rossi, J.D. "Asymptotic simplification for a reaction-diffusion problem with a nonlinear boundary condition" . IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications), vol. 67, no. 1, 2002, pp. 69-98.
http://dx.doi.org/10.1093/imamat/67.1.69
---------- VANCOUVER ----------
De Pablo, A., Quirós, F., Rossi, J.D. Asymptotic simplification for a reaction-diffusion problem with a nonlinear boundary condition. IMA J Appl Math. 2002;67(1):69-98.
http://dx.doi.org/10.1093/imamat/67.1.69