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: | , |
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| Formato: | JOUR |
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00442275_v48_n5_p711_Acosta |
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| Sumario: | 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). |
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