Some remarks on segregation of $k$ species in strongly competing systems [PDF]
Interfaces and free boundaries (Print), 2021 Spatial segregation occurs in population dynamics when k species interact in a highly competitive way. As a model for the study of this phenomenon, we consider the competitiondiffusion system of k differential equations −∆ui(x) = −μui(x) ∑ j 6=i uj(x) i =
F. Lanzara, Eugenio Montefusco
semanticscholar +1 more source
On the Asymptotic Behavior of D-Solutions to the Displacement Problem of Linear Elastostatics in Exterior Domains [PDF]
, 2020 We study the asymptotic behavior of solutions with finite energy to the displacement problem of linear elastostatics in a three-dimensional exterior Lipschitz ...
Coscia, Vincenzo
core +1 more source
Positive solution for a class of coupled (p,q)-Laplacian nonlinear systems
Boundary Value Problems, 2014 In this article, we prove the existence of a nontrivial positive solution for the elliptic system {−Δpu=ω(x)f(v)in Ω,−Δqv=ρ(x)g(u)in Ω,(u,v)=(0,0)on ∂Ω, where Δp denotes the p-Laplacian operator, p,q>1 and Ω is a smooth bounded domain in RN (N≥2).
E. M. Martins, W. Ferreira
semanticscholar +2 more sources
A generalization of the Hopf-Cole transformation for stationary Mean Field Games systems [PDF]
, 2015 In this note we propose a transformation which decouples stationary Mean Field Games systems with superlinear Hamiltonians of the form |p|^r, and turns the Hamilton-Jacobi-Bellman equation into a quasi-linear equation involving the r-Laplace operator ...
Cirant, Marco
core +3 more sources
Analytical validation of the finite element method model for Laplace equation
Journal of Applied Mathematics and Computational Mechanics, 2019 The presented paper is focused on the comparison of the numerical solution of the Laplace equation in a two-dimensional space with the results obtained with the use of the analytical method.
E. Wegrzyn-Skrzypczak, T. Skrzypczak
semanticscholar +1 more source
Asymptotic analysis for some linear eigenvalue problems via Gamma-Convergence
Advances in Differential Equations, 2010 This paper is devoted to the analysis of the asymptotic behaviour when the parameter λ goes to +∞ for operators of the form −∆+λa or more generally, cooperative systems operators of the form (−∆+λa −b −c −∆+λd ) where the potentials a and d vanish in ...
P. Álvarez-Caudevilla, A. Lemenant
semanticscholar +1 more source
Pohozhaev and Morawetz Identities in Elastostatics and Elastodynamics [PDF]
, 2011 We construct identities of Pohozhaev type, in the context of elastostatics and elastodynamics, by using the Noetherian approach. As an application, a non-existence result for forced semi-linear isotropic and anisotropic elastic systems is ...
Bozhkov, Yuri, Olver, Peter J.
core +5 more sources
$L^p$ solvability of the Stationary Stokes problem on domains with conical singularity in any dimension [PDF]
, 2010 The Dirichlet boundary value problem for the Stokes operator with $L^p$ data in any dimension on domains with conical singularity (not necessary a Lipschitz graph) is considered.
Dindoš, Martin, Maz'ya, Vladimir
core +2 more sources
A Priori Bounds And Existence Of Positive Solutions For Semilinear Elliptic Systems [PDF]
, 2017 We provide a-priori L∞ bounds for classical positive solutions of semilinear elliptic systems in bounded convex domains when the nonlinearities are below the power functions v^p and u^q for any (p,q) lying on the critical Sobolev hyperbola.
Mavinga, Nsoki, Pardo, R.
core +2 more sources
Separation of Coupled Systems of Schrodinger Equations by Darboux transformations
, 2011 Darboux transformations in one independent variable have found numerous applications in various field of mathematics and physics. In this paper we show that the extension of these transformations to two dimensions can be used to decouple systems of ...
Magri F. +3 more
core +1 more source