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On existence and nonexistence in the large for an \(N\)-dimensional system of heat equations with nontrivial coupling at the boundary. (English) Zbl 0891.35053

A system of heat equations with nonlinear boundary conditions is studied. A necessary and sufficient condition for global existence of positive solutions is given. The same result appeared before in M. Wang and Y. Wang [Sci. China, Ser. A 39, No. 8, 834-840 (1996; Zbl 0861.35043)].

MSC:

35K50 Systems of parabolic equations, boundary value problems (MSC2000)
35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
35B40 Asymptotic behavior of solutions to PDEs

Citations:

Zbl 0861.35043
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