Blow-up vs. global existence for quasilinear parabolic systems with a nonlinear boundary condition

We study the behavior of positive solutions of the system ut = div(a(u)∇u) + f(u, v) vt = div(b(v)∇u) + g(u, v) in Ω a bounded domain with the boundary conditions ∂u/∂η = r(u, v), ∂v/∂η = s(u, v) on ∂Ω and the initial data (u0, v0). We find conditions on the functions a, b, f, g, r, s that guarantee...

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Autores principales: Acosta, G., Rossi, J.D.
Formato: JOUR
Materias:
Blow up
Global existence
Nonlinear boundary conditions
Parabolic systems
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00442275_v48_n5_p711_Acosta
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_00442275_v48_n5_p711_Acosta
record_format dspace
spelling todo:paper_00442275_v48_n5_p711_Acosta2023-10-03T14:51:35Z Blow-up vs. global existence for quasilinear parabolic systems with a nonlinear boundary condition Acosta, G. Rossi, J.D. Blow up Global existence Nonlinear boundary conditions Parabolic systems We study the behavior of positive solutions of the system ut = div(a(u)∇u) + f(u, v) vt = div(b(v)∇u) + g(u, v) in Ω a bounded domain with the boundary conditions ∂u/∂η = r(u, v), ∂v/∂η = s(u, v) on ∂Ω and the initial data (u0, v0). We find conditions on the functions a, b, f, g, r, s that guarantee the global existence (or finite time blow-up) of positive solutions for every (u0, v0). Fil:Acosta, G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Rossi, J.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00442275_v48_n5_p711_Acosta
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Blow up
Global existence
Nonlinear boundary conditions
Parabolic systems
spellingShingle Blow up
Global existence
Nonlinear boundary conditions
Parabolic systems
Acosta, G.
Rossi, J.D.
Blow-up vs. global existence for quasilinear parabolic systems with a nonlinear boundary condition
topic_facet Blow up
Global existence
Nonlinear boundary conditions
Parabolic systems
description We study the behavior of positive solutions of the system ut = div(a(u)∇u) + f(u, v) vt = div(b(v)∇u) + g(u, v) in Ω a bounded domain with the boundary conditions ∂u/∂η = r(u, v), ∂v/∂η = s(u, v) on ∂Ω and the initial data (u0, v0). We find conditions on the functions a, b, f, g, r, s that guarantee the global existence (or finite time blow-up) of positive solutions for every (u0, v0).
format JOUR
author Acosta, G.
Rossi, J.D.
author_facet Acosta, G.
Rossi, J.D.
author_sort Acosta, G.
title Blow-up vs. global existence for quasilinear parabolic systems with a nonlinear boundary condition
title_short Blow-up vs. global existence for quasilinear parabolic systems with a nonlinear boundary condition
title_full Blow-up vs. global existence for quasilinear parabolic systems with a nonlinear boundary condition
title_fullStr Blow-up vs. global existence for quasilinear parabolic systems with a nonlinear boundary condition
title_full_unstemmed Blow-up vs. global existence for quasilinear parabolic systems with a nonlinear boundary condition
title_sort blow-up vs. global existence for quasilinear parabolic systems with a nonlinear boundary condition
url http://hdl.handle.net/20.500.12110/paper_00442275_v48_n5_p711_Acosta
work_keys_str_mv AT acostag blowupvsglobalexistenceforquasilinearparabolicsystemswithanonlinearboundarycondition
AT rossijd blowupvsglobalexistenceforquasilinearparabolicsystemswithanonlinearboundarycondition
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