For the reaction-diffusion system of three competing species: -Delta u(i) = -mu mu(i) Sigma(j not equal i) u(j), i = 1, 2, 3, we prove uniqueness of the limiting configuration as mu --> infinity on a planar domain Omega, with appropriate boundary conditions. Moreover we prove that the limiting configuration minimizes the energy associated to the system E(U) = Sigma(3)(i=1) integral(Omega) \del u(i)(x)\(2) dx among all segregated states (u(i) . u(j) = 0 a. e.) with the same boundary conditions
Conti, M., Terracini, S., Verzini, G. (2006). Uniqueness and least energy property for solutions to strongly competing systems. INTERFACES AND FREE BOUNDARIES, 8(4), 437-446 [10.4171/IFB/150].
Uniqueness and least energy property for solutions to strongly competing systems
Terracini, S;
2006
Abstract
For the reaction-diffusion system of three competing species: -Delta u(i) = -mu mu(i) Sigma(j not equal i) u(j), i = 1, 2, 3, we prove uniqueness of the limiting configuration as mu --> infinity on a planar domain Omega, with appropriate boundary conditions. Moreover we prove that the limiting configuration minimizes the energy associated to the system E(U) = Sigma(3)(i=1) integral(Omega) \del u(i)(x)\(2) dx among all segregated states (u(i) . u(j) = 0 a. e.) with the same boundary conditions
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