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Quantitative maximum principles and strongly coupled gradient-like reaction-diffusion systems. (English) Zbl 0538.35009
Author’s summary: ”We consider mainly a system of reaction-diffusion equations with general diffusion matrix and we establish the stabilization of all solutions at \(t\to \infty\). The interest of this problem derives from two separate facts. First, the sets that are useful for localizing the asymptotics cease to be invariant as soon as the diffusion matrix is not a multiple of the identity. Second, the set of equilibria is connected. Further, we establish uniform \(L^{\infty}\) bounds for the solutions of a class of parabolic systems. The unifying feature in the problems considered is the lack of any conventional maximum principles.”
Reviewer: A.D.Osborne

MSC:
35B50 Maximum principles in context of PDEs
35B40 Asymptotic behavior of solutions to PDEs
35K55 Nonlinear parabolic equations
35J45 Systems of elliptic equations, general (MSC2000)
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