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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todo:paper_01704214_v20_n1_p1_Rossi2023-10-03T15:07:25Z The blow-up rate for a system of heat equations with non-trivial coupling at the boundary Rossi, J.D. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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, J.D. 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. |
| format |
JOUR |
| author |
Rossi, J.D. |
| author_facet |
Rossi, J.D. |
| author_sort |
Rossi, J.D. |
| 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 |
| url |
http://hdl.handle.net/20.500.12110/paper_01704214_v20_n1_p1_Rossi |
| work_keys_str_mv |
AT rossijd theblowuprateforasystemofheatequationswithnontrivialcouplingattheboundary AT rossijd blowuprateforasystemofheatequationswithnontrivialcouplingattheboundary |
| _version_ |
1807316069795233792 |