204 citations · 508 across the 19 of their papers we have counts for
19 papers
Ground states of a nonlocal variational problem and Thomas-Fermi limit for the Choquard equation
Damiano Greco, Yanghong Huang, Zeng Liu +1
We study nonnegative optimizers of a Gagliardo-Nirenberg type inequality $$\iint_{\mathbb{R}^N \times \mathbb{R}^N} \frac{|u(x)|^p\,|u(y)|^p}{|x - y|^{N-α}} dx\, dy\le C\Big(\int_{…
Nonlinear aggregation-diffusion equations with Riesz potentials
Yanghong Huang, Edoardo Mainini, Juan Luis Vázquez +1
We consider an aggregation-diffusion model, where the diffusion is nonlinear of porous medium type and the aggregation is governed by the Riesz potential of order s. The addition o…
Uniqueness of entire ground states for the fractional plasma problem
Hardy Chan, María del Mar González, Yanghong Huang +2
We establish uniqueness of vanishing radially decreasing entire solutions, which we call ground states, to some semilinear fractional elliptic equations. In particular, we treat th…
Long-time asymptotics for nonlocal porous medium equation with absorption or convection
Filomena Feo, Yanghong Huang, Bruno Volzone
In this paper, the long-time asymptotic behaviours of nonlocal porous medium equations with absorption or convection are studied. In the parameter regimes when the nonlocal diffusi…
Fokker-Planck equation driven by asymmetric Lévy motion
Xiao Wang, Wenpeng Shang, Xiaofan Li +2
Non-Gaussian Lévy noises are present in many models for understanding underlining principles of physics, finance, biology and more. In this work, we consider the Fokker-Planck equa…
Zoology of a non-local cross-diffusion model for two species
J. A. Carrillo, Y. Huang, M. Schmidtchen
We study a non-local two species cross-interaction model with cross-diffusion. We propose a positivity preserving finite volume scheme based on the numerical method introduced in R…
Finite Difference Methods for the generator of 1D asymmetric alpha-stable Lévy motions
Yanghong Huang, Xiao Wang
Several finite difference methods are proposed for the infinitesimal generator of 1D asymmetric -stable Lévy motions, based on the fact that the operator becomes a multiplier in…
Finite difference methods for fractional Laplacians
Yanghong Huang, Adam Oberman
The fractional Laplacian is the prototypical non-local elliptic operator. While analytical theory has been advanced and understood for some time, there remain many ope…
Explicit Equilibrium Solutions For the Aggregation Equation with Power-Law Potentials
José A. Carrillo, Yanghong Huang
Despite their wide presence in various models in the study of collective behaviors, explicit swarming patterns are difficult to obtain. In this paper, special stationary solutions…
Numerical Study of a Particle Method for Gradient Flows
J. A. Carrillo, Y. Huang, F. S. Patacchini +1
We study the numerical behaviour of a particle method for gradient flows involving linear and nonlinear diffusion. This method relies on the discretisation of the energy via non-ov…
Exponential Convergence Towards Stationary States for the 1D Porous Medium Equation with Fractional Pressure
J. A. Carrillo, Y. Huang, M. C. Santos +1
We analyse the asymptotic behaviour of solutions to the one dimensional fractional version of the porous medium equation introduced by Caffarelli and Vázquez, where the pressure is…
On global minimizers of repulsive-attractive power-law interaction energies
José Antonio Carrillo, Michel Chipot, Yanghong Huang
We consider the minimisation of power-law repulsive-attractive interaction energies which occur in many biological and physical situations. We show existence of global minimizers i…
A Finite-Volume Method for Nonlinear Nonlocal Equations with a Gradient Flow Structure
José A. Carrillo, Alina Chertock, Yanghong Huang
We propose a positivity preserving entropy decreasing finite volume scheme for nonlinear nonlocal equations with a gradient flow structure. These properties allow for accurate comp…
Explicit Barenblatt Profiles for Fractional Porous Medium Equations
Yanghong Huang
Several one-parameter families of explicit self-similar solutions are constructed for the porous medium equations with fractional operators. The corresponding self-similar profiles…
Numerical Methods for the Fractional Laplacian: a Finite Difference-quadrature Approach
Yanghong Huang, Adam Oberman
The fractional Laplacian is a non-local operator which depends on the parameter and recovers the usual Laplacian as . A numerical method for the fractional…
Nonlinear stability of flock solutions in second-order swarming models
J. A. Carrillo, Y. Huang, S. Martin
In this paper we consider interacting particle systems which are frequently used to model collective behavior in animal swarms and other applications. We study the stability of ori…
Explicit Flock Solutions for Quasi-Morse potentials
Jose Antonio Carrillo, Yanghong Huang, Stephan Martin
We consider interacting particle systems and their mean-field limits, which are frequently used to model collective aggregation and are known to demonstrate a rich variety of patte…
Stationary States and Asymptotic Behaviour of Aggregation Models with Nonlinear Local Repulsion
Martin Burger, Razvan Fetecau, Yanghong Huang
We consider a continuum aggregation model with nonlinear local repulsion given by a degenerate power-law diffusion with general exponent. The steady states and their properties in…
Equilibria of biological aggregations with nonlocal repulsive-attractive interactions
R. C. Fetecau, Y. Huang
We consider the aggregation equation in , where the interaction potential incorporates short-range Newtonian repulsion an…