204 citations · 508 across the 19 of their papers we have counts for
12 papers · 1 filter
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…
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…
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…
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…
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…