Asymptotic estimates for the spatial segregation of competitive systems

By Monica Conti, S. Terracini, Gianmaria Verzini. 2005

198 citations recorded by the source corpus.

Subfields: Applied Mathematics, Modeling and Simulation, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/029abbe6999204c2a7cf19bd1fd3eb8bacc07bf6

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Modeling and Simulation

In Public Health, Environmental and Occupational Health

Citations in the corpus

Some Challenging Mathematical Problems in Evolution of Dispersal and Population Dynamics (2008, background): “For the last two decades there has been tremendous interest, by both mathematicians and ecologists, in two-species Lotka-Volterra competition models with spatially homogeneous or heterogeneous interactions, see [9, 10, 11, 12, 18, 19, 28, 29, 33, 35, 38, 39, 40, 41, 46, 55, 59, 62, 63, 64, 65, 66, 7”
A minimization problem with free boundary related to a cooperative system (2016, background): “pui= supuj for some of these i,j.2 Those gi that are still 1Competitive systems, which gives rise to disjoint support of limiting solutions, have been much in focus in the last decade (see e.g. [10], [11]). Competitive system of more than two equations usually give rise to the so-called junction poi”
On Phase-Separation Models: Asymptotics and Qualitative Properties (2013, methodology): “One may refer to Chang-Lin-Lin-Lin [17] for the pointwise convergence of (u Λ , v Λ ) away from the interface γ ≡ {x ∈ Ω : u ∞ (x) = v ∞ (x) = 0}; Wei-Weth [46] for the uniform equicontinuity of (u Λ , v Λ ); and Noris-Tavares-Terracini-Verzini [39] for the uniform Hölder continuity of (u Λ , v Λ ).”
Uniform Hölder Estimates in a Class of Elliptic Systems and Applications to Singular Limits in Models for Diffusion Flames (2007, background): “The difference between Theorem 1 and [ 10 ] is in the fact that a uniform Lipschitz regularity need not be true in system 1, unless some compatibility assumption between the matrices A k := (a k ) is made (see Section 5 below).”
Radial Solutions and Phase Separation in a System of Two Coupled Schrödinger Equations (2008, background): “Property (ii) is just a consequence of the parabolic maximum principle, since u and v both satisfy equations of the form wt −∆w = f(x, t)w in B with locally bounded f , together with homogeneous Dirichlet boundary conditions.”
Uniform Bounds for Strongly Competing Systems: The Optimal Lipschitz Case (2014, background): “Theorem (Conti, Terracini, Verzini, [13]).”
Positive Least Energy Solutions and Phase Separation for Coupled Schrödinger Equations with Critical Exponent (2012, background): “For other kinds of elliptic systems with strong competition, phase separation has also been well studied, we refer to [10, 11, 14] and references therein.”
Positive least energy solutions and phase separation for coupled Schrödinger equations with critical exponent: higher dimensional case (2015, background): “For other kinds of elliptic systems with strong competition, phase separation has also been well studied, we refer to [10,11,17] and references therein.”
Dynamics of strongly competing systems with many species (2012, methodology): “Conti, Terracini and Verzini [9], [10], Caffarelli, Karakhanyan and Lin [2] [3], etc.”
The geometry of solutions to a segregation problem for nondivergence systems (2009, background): “This problem has received a considerable attention in particular [CTV][CTV2] [ CTV3 ][CTV4] vari-”
On a class of optimal partition problems related to the Fučík spectrum and to the monotonicity formulae (2003, methodology): “The subsequent Liouville type result will be exploited, in a forthcoming paper [ 9 ], in order to prove the uniform h¨ older-continuity of solutions of competition–diffusion systems, when the interspecific competition rate tends to infinity.”