Strong Competition versus Fractional Diffusion: The Case of Lotka-Volterra Interaction

DOI10.1080/03605302.2014.890627zbMath1327.35418arXiv1310.7355OpenAlexW1981427622MaRDI QIDQ2931985

Alessandro Zilio, Gianmaria Verzini

Publication date: 28 November 2014

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1310.7355

zbMATH Keywords

singular perturbationsblow-up analysismonotonicity formulaespatial segregationoptimal regularity of limiting profiles

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Population dynamics (general) (92D25) Blow-up in context of PDEs (35B44) Fractional partial differential equations (35R11)

Related Items

On the uniqueness of solutions of a nonlocal elliptic system ⋮ Some monotonicity results for general systems of nonlinear elliptic PDEs ⋮ Symmetry of components and Liouville-type theorems for semilinear elliptic systems involving the fractional Laplacian ⋮ Segregated configurations involving the square root of the Laplacian and their free boundaries ⋮ Free boundary problems with long-range interactions: uniform Lipschitz estimates in the radius ⋮ An anisotropic monotonicity formula, with applications to some segregation problems ⋮ A priori estimates and Liouville type theorems for semilinear equations and systems with fractional Laplacian ⋮ Uniform bounds for strongly competing systems: the optimal Lipschitz case ⋮ Uniform Hölder bounds for strongly competing systems involving the square root of the Laplacian ⋮ Regularity results for segregated configurations involving fractional Laplacian ⋮ Variational problems with long-range interaction ⋮ Uniqueness and least energy property for solutions to a strongly coupled elliptic system ⋮ Nodal set of strongly competition systems with fractional Laplacian

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