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We give a simple and direct proof of the characterization of positivity preserving semi-flows for ordinary differential systems. The same method provides an abstract result on a class of evolution systems containing reaction-diffusion systems in a bounded domain of $ \mathbb{R}^n$ with either Neumann or Dirichlet homogeneous boundary conditions. The conditions are exactly the same with or without diffusion. A similar approach gives the optimal result for invariant rectangles in the case of Neumann conditions.
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참고문헌 (11)
참고문헌 신청
A. Barabanova / 1994 / On the global existence of solutions of a reaction-diffusion equation with exponential nonlinearity / Proc. Amer. Math. Soc 122 (3) : 827 ~ 831
A. Haraux / 1983 / Estimations C1 pour des problemes paraboliques semi-lin'eaires, (French. English summary) [C1 estimates for semilinear parabolic problems] / Ann. Fac. Sci.
A. Haraux / 1988 / On a result of K. Masuda concerning reaction-diffusion equations / Tohoku Math. J. 2 40 (1) : 159 ~ 163
G. Bourceanu / 1985 / The study of the evolution of some self-organized chemical systems / J. Chemical Phys 82 : 3685 ~ 3691
H. Brezis / 1970 / On a characterization of flow-invariant sets / Comm. Pure Appl. Math 23 : 261 ~ 263
A. Haraux / 1983 / Estimations C1 pour des problemes paraboliques semi-lin'eaires, (French. English summary) [C1 estimates for semilinear parabolic problems] / Ann. Fac. Sci.
A. Haraux / 1988 / On a result of K. Masuda concerning reaction-diffusion equations / Tohoku Math. J. 2 40 (1) : 159 ~ 163
G. Bourceanu / 1985 / The study of the evolution of some self-organized chemical systems / J. Chemical Phys 82 : 3685 ~ 3691
H. Brezis / 1970 / On a characterization of flow-invariant sets / Comm. Pure Appl. Math 23 : 261 ~ 263
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