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Abstract:

We study the blow-up rate of positive radial solutions of a system of two heat equations, (U1)t = Δu1(u2)t = Δu2, in the ball B(0,1), with boundary conditions equation presenteded Under some natural hypothesis on the matrix P = (pij) that guarrantee the blow-up of the solution at time T, and some assumptions of the initial data uoi, we find that if ∥x0∥ = 1 then ui-(x0, t)goestoinfinity-like(T - t)αi/2, where the αi < 0 are the solutions of (P - Id) (α1, α2)t = (-1, -1)t. As a corollary of the blow-up rate we obtain the loclaization of the blow-up set at the boundary of the domain.

Registro:

Documento: Artículo
Título:The blow-up rate for a system of heat equations with non-trivial coupling at the boundary
Autor:Rossi, J.D.
Filiación:Departamento de Matemática, Fac. de Ciencias Exactas y Naturales, Universidad de Buenos Aires, (1428) Buenos Aires, Argentina
Palabras clave:Boundary conditions; Equations of state; Matrix algebra; Problem solving; Set theory; Blow up rate; Heat equations; Mathematical techniques
Año:1997
Volumen:20
Número:1
Página de inicio:1
Página de fin:11
DOI: http://dx.doi.org/10.1002/(SICI)1099-1476(19970110)20:1<1::AID-MMA843>3.0.CO;2-E
Título revista:Mathematical Methods in the Applied Sciences
Título revista abreviado:Math Methods Appl Sci
ISSN:01704214
CODEN:MMSCD
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01704214_v20_n1_p1_Rossi

Referencias:

  • Acosta, G., Rossi, J.D., (1995) Blow-up Vs. Global Existence for Quasilinear Parabolic Systems with a Nonlinear Boundary Condition, , preprint
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  • Rial, D.F., Rossi, J.D., (1995) Blow-up Results and Localization of Blow-up Points in An N-dimensional Smooth Domain, , Preprint
  • Rial, D.F., Rossi, J.D., (1996) Localization of Blow-up Points for a Parabolic System with Nonlinear Boundary Condition, , Preprint
  • Rossi, J.D., (1995) On Existence and Nonexistence in the Large, for An N-dimensional System of Heat Equations with Nontrivial Coupling at the Boundary, , Preprint
  • Rossi, J.D., Wolanski, N., Global existence and nonexistence for a parabolic system with nonlinear boundary conditions Diff. Int. Eq., , to appear
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Citas:

---------- APA ----------
(1997) . The blow-up rate for a system of heat equations with non-trivial coupling at the boundary. Mathematical Methods in the Applied Sciences, 20(1), 1-11.
http://dx.doi.org/10.1002/(SICI)1099-1476(19970110)20:1<1::AID-MMA843>3.0.CO;2-E
---------- CHICAGO ----------
Rossi, J.D. "The blow-up rate for a system of heat equations with non-trivial coupling at the boundary" . Mathematical Methods in the Applied Sciences 20, no. 1 (1997) : 1-11.
http://dx.doi.org/10.1002/(SICI)1099-1476(19970110)20:1<1::AID-MMA843>3.0.CO;2-E
---------- MLA ----------
Rossi, J.D. "The blow-up rate for a system of heat equations with non-trivial coupling at the boundary" . Mathematical Methods in the Applied Sciences, vol. 20, no. 1, 1997, pp. 1-11.
http://dx.doi.org/10.1002/(SICI)1099-1476(19970110)20:1<1::AID-MMA843>3.0.CO;2-E
---------- VANCOUVER ----------
Rossi, J.D. The blow-up rate for a system of heat equations with non-trivial coupling at the boundary. Math Methods Appl Sci. 1997;20(1):1-11.
http://dx.doi.org/10.1002/(SICI)1099-1476(19970110)20:1<1::AID-MMA843>3.0.CO;2-E