Zobrazeno 1 - 10
of 66
pro vyhledávání: '"Huang, Yanghong"'
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-\alpha}} dx\, dy\le C\Big(\int_{{\mathbb R}^N}|u|^2 dx\Big)^{p\theta} \Big(\int_{{\mathbb R}^N}|u
Externí odkaz:
http://arxiv.org/abs/2406.18472
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 of a quadratic diffusion term produces a more precise competition with
Externí odkaz:
http://arxiv.org/abs/2205.13520
Publikováno v:
In Journal of Functional Analysis 15 July 2024 287(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 the fractional plasma equation and the supercritical power nonlinearity.
Externí odkaz:
http://arxiv.org/abs/2003.01093
Publikováno v:
Commun. Contemp. Math. 22, No. 3, Article ID 1950015, 32 p. (2020)
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 diffusion is dominant, the entropy method is adapted in this context to deriv
Externí odkaz:
http://arxiv.org/abs/1803.01697
Non-Gaussian L\'evy noises are present in many models for understanding underlining principles of physics, finance, biology and more. In this work, we consider the Fokker-Planck equation(FPE) due to one-dimensional asymmetric L\'evy motion, which is
Externí odkaz:
http://arxiv.org/abs/1803.00923
Autor:
Huang, Yanghong, Wang, Xiao
Several finite difference methods are proposed for the infinitesimal generator of 1D asymmetric $\alpha$-stable L\'{e}vy motions, based on the fact that the operator becomes a multiplier in the spectral space. These methods take the general form of a
Externí odkaz:
http://arxiv.org/abs/1705.03357
Autor:
Huang, Yanghong, Oberman, Adam
The fractional Laplacian $(-\Delta)^{\alpha/2}$ is the prototypical non-local elliptic operator. While analytical theory has been advanced and understood for some time, there remain many open problems in the numerical analysis of the operator. In thi
Externí odkaz:
http://arxiv.org/abs/1611.00164
Autor:
Carrillo, José A., Huang, Yanghong
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 of the aggregation equation with power-law kernels are constructed by
Externí odkaz:
http://arxiv.org/abs/1602.06615
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 in the discrete setting and get bounds for their supports independently
Externí odkaz:
http://arxiv.org/abs/1403.7420