The Experts below are selected from a list of 315 Experts worldwide ranked by ideXlab platform
Mingxin Wang - One of the best experts on this subject based on the ideXlab platform.
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systems with nonlocal vs local diffusions and Free Boundaries
Journal of Mathematical Analysis and Applications, 2020Co-Authors: Lei Li, Mingxin Wang, Weijie ShengAbstract:Abstract We study a class of Free boundary problems of ecological models with nonlocal and local diffusions, which are natural extensions of Free boundary problems of reaction diffusion systems in there local diffusions are used to describe the population dispersal, with the Free boundary representing the spreading front of the species. We first prove the existence, uniqueness and regularity of global solution. For the classical competition, prey-predator and mutualist models, we show that a spreading-vanishing dichotomy holds, and establish the criteria of spreading and vanishing, and long time behavior of the solution.
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dynamics for a diffusive prey predator model with different Free Boundaries
Journal of Differential Equations, 2018Co-Authors: Mingxin Wang, Yang ZhangAbstract:Abstract To understand the spreading and interaction of prey and predator, in this paper we study the dynamics of the diffusive Lotka–Volterra type prey–predator model with different Free Boundaries. These two Free Boundaries, which may intersect each other as time evolves, are used to describe the spreading of prey and predator. We investigate the existence and uniqueness, regularity and uniform estimates, and long time behaviors of global solution. Some sufficient conditions for spreading and vanishing are established. When spreading occurs, we provide the more accurate limits of ( u , v ) as t → ∞ , and give some estimates of asymptotic spreading speeds of u , v and asymptotic speeds of g , h . Some realistic and significant spreading phenomena are found.
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a Free boundary problem for the predator prey model with double Free Boundaries
Journal of Dynamics and Differential Equations, 2017Co-Authors: Mingxin Wang, Jingfu ZhaoAbstract:In this paper we investigate a Free boundary problem for the classical Lotka–Volterra type predator–prey model with double Free Boundaries in one space dimension. This system models the expanding of an invasive or new predator species in which the Free Boundaries represent expanding fronts of the predator species and are described by Stefan-like condition. We prove a spreading–vanishing dichotomy for this model, namely the predator species either successfully spreads to infinity as \(t\rightarrow \infty \) at both fronts and survives in the new environment, or it spreads within a bounded area and dies out in the long run while the prey species stabilizes at a positive equilibrium state. The long time behavior of solution and criteria for spreading and vanishing are also obtained.
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A Free Boundary Problem for the Predator–Prey Model with Double Free Boundaries
Journal of Dynamics and Differential Equations, 2017Co-Authors: Mingxin Wang, Jingfu ZhaoAbstract:In this paper we investigate a Free boundary problem for the classical Lotka–Volterra type predator–prey model with double Free Boundaries in one space dimension. This system models the expanding of an invasive or new predator species in which the Free Boundaries represent expanding fronts of the predator species and are described by Stefan-like condition. We prove a spreading–vanishing dichotomy for this model, namely the predator species either successfully spreads to infinity as \(t\rightarrow \infty \) at both fronts and survives in the new environment, or it spreads within a bounded area and dies out in the long run while the prey species stabilizes at a positive equilibrium state. The long time behavior of solution and criteria for spreading and vanishing are also obtained.
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note on a two species competition diffusion model with two Free Boundaries
Nonlinear Analysis-theory Methods & Applications, 2017Co-Authors: Mingxin Wang, Yang ZhangAbstract:Abstract In Guo and Wu (2015) and Wu (2015), the authors studied a two-species competition-diffusion model with two Free Boundaries. These two Free Boundaries describing the spreading fronts of two competing species, respectively, may intersect each other as time evolves. The existence, uniqueness and long time behavior of global solution have been established. In this note we discuss the conditions for spreading and vanishing, and more accurate limits of ( u , v ) as t → ∞ when spreading occurs. Some new results and simpler proofs will be provided.
Luis A Caffarelli - One of the best experts on this subject based on the ideXlab platform.
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obstacle problems for integro differential operators regularity of solutions and Free Boundaries
Inventiones Mathematicae, 2017Co-Authors: Luis A Caffarelli, Xavier Rosoton, Joaquim SerraAbstract:We study the obstacle problem for integro-differential operators of order 2s, with \(s\in (0,1)\). Our main result establish that the Free boundary is \(C^{1,\gamma }\) and \(u\in C^{1,s}\) near all regular points. Namely, we prove the following dichotomy at all Free boundary points \(x_0\in \partial \{u=\varphi \}\): (i) either \(u(x)-\varphi (x)=c\,d^{1+s}(x)+o(|x-x_0|^{1+s+\alpha })\) for some \(c>0\), (ii) or \(u(x)-\varphi (x)=o(|x-x_0|^{1+s+\alpha })\), where d is the distance to the contact set \(\{u=\varphi \}\). Moreover, we show that the set of Free boundary points \(x_0\) satisfying (i) is open, and that the Free boundary is \(C^{1,\gamma }\) and \(u\in C^{1,s}\) near those points. These results were only known for the fractional Laplacian [2], and are completely new for more general integro-differential operators. The methods we develop here are purely nonlocal, and do not rely on any monotonicity-type formula for the operator. Thanks to this, our techniques can be applied in the much more general context of fully nonlinear integro-differential operators: we establish similar regularity results for obstacle problems with convex operators.
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regularity of Free Boundaries a heuristic retro
Philosophical Transactions of the Royal Society A, 2015Co-Authors: Luis A Caffarelli, Henrik ShahgholianAbstract:This survey concerns regularity theory of a few Free boundary problems that have been developed in the past half a century. Our intention is to bring up different ideas and techniques that constitute the fundamentals of the theory. We shall discuss four different problems, where approaches are somewhat different in each case. Nevertheless, these problems can be divided into two groups: (i) obstacle and thin obstacle problem; (ii) minimal surfaces, and cavitation flow of a perfect fluid. In each case, we shall only discuss the methodology and approaches, giving basic ideas and tools that have been specifically designed and tailored for that particular problem. The survey is kept at a heuristic level with mainly geometric interpretation of the techniques and situations in hand.
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variational problems with Free Boundaries for the fractional laplacian
Journal of the European Mathematical Society, 2010Co-Authors: Luis A Caffarelli, Jeanmichel Roquejoffre, Yannick SireAbstract:We discuss properties (optimal regularity, non-degeneracy, smoothness of the Free boundary...) of a variational interface problem involving the fractional Laplacian; Due to the non-locality of the Dirichlet problem, the task is nontrivial. This difficulty is by-passed by an extension formula, discovered by the first author and Silvestre, which reduces the study to that of a co-dimension 2 (degenerate) Free boundary.
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Free Boundaries in optimal transport and monge ampere obstacle problems
Annals of Mathematics, 2010Co-Authors: Luis A Caffarelli, Robert J MccannAbstract:Given compactly supported 0 f,g 2 L 1 (R n ), the problem of trans- porting a fraction m min{kfkL1,kgkL1} of the mass of f onto g as cheaply as possible is considered, where cost per unit mass transported is given by a cost function c, typically quadratic c(x,y) = |x y| 2 /2. This question is shown to be equivalent to a double obstacle problem for the Monge-Ampere equation, for which sucient conditions are given to guarantee uniqueness of the solution, such as f vanishing on sptg in the quadratic case. The part of f to be transported increases monotonically with m, and if sptf and sptg are separated by a hyperplane H, then this part will separated from the balance of f by a semiconcave Lipschitz graph over the hyperplane. If f = f and g = g are bounded away from zero and infinity on separated strictly convex domains , R n , for the quadratic cost this graph is shown to be a C 1, loc hypersurface in whose normal coincides with the direction transported; the optimal map between f and g is shown to be Holder continuous up to this Free bound- ary, and to those parts of the fixed boundary @ which map to locally convex parts of the path-connected target region.
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singularly perturbed elliptic systems and multi valued harmonic functions with Free Boundaries
Journal of the American Mathematical Society, 2008Co-Authors: Luis A CaffarelliAbstract:Here we study the asymptotic limits of solutions of some singularly perturbed elliptic systems. The limiting problems involve multiple valued harmonic functions or, in general, harmonic maps to singular spaces and Free interfaces between supports of various components of the maps. The main results of the paper are the uniform Lipschitz regularity of solutions as well as the regularity of Free interfaces.
Peiyong Wang - One of the best experts on this subject based on the ideXlab platform.
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REGULARITY OF Free Boundaries OF TWO-PHASE PROBLEMS FOR FULLY NONLINEAR ELLIPTIC EQUATIONS OF SECOND ORDER. II. FLAT Free Boundaries ARE LIPSCHITZ
Communications in Partial Differential Equations, 2002Co-Authors: Peiyong WangAbstract:ABSTRACT In this second paper, we continue our study on the regularity of Free Boundaries for some fully nonlinear elliptic equations. Our result is if the Free boundary is trapped in a sufficiently narrow strip formed by two Lipschitz graphs, then it is also a Lipschitz graph. Combining with the results in Part 1 (see Ref. [Wang]), the Free boundary is C 1,α.
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regularity of Free Boundaries of two phase problems for fully nonlinear elliptic equations of second order i lipschitz Free Boundaries are c1 α
Communications on Pure and Applied Mathematics, 2000Co-Authors: Peiyong WangAbstract:In this paper, we study an extension of a C1,α regularity theory developed by L. Caffarelli in [2] to some fully nonlinear elliptic equations of second order. In fact, we investigate a two-phase Free boundary problem in which a fully nonlinear elliptic equation of second order is verified by the solution in the positive and the negative domains. Assuming the Free boundary is locally a Lipschitz graph, we have established the C1,α regularity of the Free boundary. © 2000 John Wiley & Sons, Inc.
Arman Melkumyan - One of the best experts on this subject based on the ideXlab platform.
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twelve shear surface waves guided by clamped Free Boundaries in magneto electro elastic materials
International Journal of Solids and Structures, 2007Co-Authors: Arman MelkumyanAbstract:It is shown that surface waves with 12 different velocities in the cases of different magneto-electrical boundary conditions can be guided by the interface of two identical magneto-electro-elastic half-spaces. The plane boundary of one of the half-spaces is clamped while the plane boundary of the other one is Free of stresses. The 12 velocities of propagation of these surface waves are obtained is explicit forms. It is shown that the number of different surface wave velocities decreases from 12 to 2 if the magneto-electro-elastic material is changed to a piezoelectric material.
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twelve shear surface waves guided by clamped Free Boundaries in magneto electro elastic materials
arXiv: General Physics, 2006Co-Authors: Arman MelkumyanAbstract:It is shown that surface waves with twelve different velocities in the cases of different magneto-electrical boundary conditions can be guided by the interface of two identical magneto-electro-elastic half-spaces. The plane boundary of one of the half-spaces is clamped while the plane boundary of the other one is Free of stresses. The 12 velocities of propagation of these surface waves are obtained is explicit forms. It is shown that the number of different surface wave velocities decreases from 12 to 2 if the magneto-electro-elastic material is changed to a piezoelectric material.
Filippo Morabito - One of the best experts on this subject based on the ideXlab platform.
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Free Boundaries surfaces and saddle towers minimal surfaces in s2 r
Journal of Mathematical Analysis and Applications, 2016Co-Authors: Filippo MorabitoAbstract:Abstract The aim of this work is to show that for each finite natural number l ⩾ 2 there exists a 1-parameter family of Saddle Tower type minimal surfaces embedded in S 2 × R , invariant with respect to a vertical translation. The genus of the quotient surface is 2 l − 1 . The proof is based on analytical techniques: precisely we desingularize of the union of γ j × R , j ∈ { 1 , … , 2 l } , where γ j ⊂ S 2 denotes a half great circle. These vertical cylinders intersect along a vertical straight line and its antipodal line. As byproduct of the construction we produce Free boundary surfaces embedded in ( S 2 ) + × R . Such surfaces are extended by reflection in ∂ ( S 2 ) + × R in order to get the minimal surfaces with the desired properties.
