The blow-up rate for a system of heat equations with non-trivial coupling at the boundary

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 as...

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Autor principal: Rossi, Julio Daniel
Publicado: 1997
Materias:
Boundary conditions
Equations of state
Matrix algebra
Problem solving
Set theory
Blow up rate
Heat equations
Mathematical techniques
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01704214_v20_n1_p1_Rossi
http://hdl.handle.net/20.500.12110/paper_01704214_v20_n1_p1_Rossi
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling paper:paper_01704214_v20_n1_p1_Rossi2023-06-08T15:18:35Z The blow-up rate for a system of heat equations with non-trivial coupling at the boundary Rossi, Julio Daniel Boundary conditions Equations of state Matrix algebra Problem solving Set theory Blow up rate Heat equations Mathematical techniques 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. Fil:Rossi, J.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 1997 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01704214_v20_n1_p1_Rossi http://hdl.handle.net/20.500.12110/paper_01704214_v20_n1_p1_Rossi
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Boundary conditions
Equations of state
Matrix algebra
Problem solving
Set theory
Blow up rate
Heat equations
Mathematical techniques
spellingShingle Boundary conditions
Equations of state
Matrix algebra
Problem solving
Set theory
Blow up rate
Heat equations
Mathematical techniques
Rossi, Julio Daniel
The blow-up rate for a system of heat equations with non-trivial coupling at the boundary
topic_facet Boundary conditions
Equations of state
Matrix algebra
Problem solving
Set theory
Blow up rate
Heat equations
Mathematical techniques
description 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.
author Rossi, Julio Daniel
author_facet Rossi, Julio Daniel
author_sort Rossi, Julio Daniel
title The blow-up rate for a system of heat equations with non-trivial coupling at the boundary
title_short The blow-up rate for a system of heat equations with non-trivial coupling at the boundary
title_full The blow-up rate for a system of heat equations with non-trivial coupling at the boundary
title_fullStr The blow-up rate for a system of heat equations with non-trivial coupling at the boundary
title_full_unstemmed The blow-up rate for a system of heat equations with non-trivial coupling at the boundary
title_sort blow-up rate for a system of heat equations with non-trivial coupling at the boundary
publishDate 1997
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01704214_v20_n1_p1_Rossi
http://hdl.handle.net/20.500.12110/paper_01704214_v20_n1_p1_Rossi
work_keys_str_mv AT rossijuliodaniel theblowuprateforasystemofheatequationswithnontrivialcouplingattheboundary
AT rossijuliodaniel blowuprateforasystemofheatequationswithnontrivialcouplingattheboundary
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