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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| Formato: | JOUR |
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_01704214_v20_n1_p1_Rossi |
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| Sumario: | 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. |
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