Rossi, Julio D. 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 N. Z. J. Math. 26, No. 2, 275-285 (1997). 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)]. Reviewer: M.Fila (Bratislava) Cited in 3 Documents 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 Keywords:nonlinear boundary conditions; global existence; blow-up Citations:Zbl 0861.35043 PDFBibTeX XMLCite \textit{J. D. Rossi}, N. Z. J. Math. 26, No. 2, 275--285 (1997; Zbl 0891.35053)