14 citations · 38 across the 49 of their papers we have counts for
12 papers · 1 filter
Sharp Fractional Sobolev Embeddings on Closed Manifolds
Hao Tan, Zetian Yan, Zhipeng Yang
We develop an intrinsic, heat-kernel based fractional Sobolev framework on closed Riemannian manifolds and study the critical fractional Sobolev embedding. We determine the optimal…
Convexification Numerical Method for Imaging of Moving Targets
Michael V. Klibanov, Jingzhi Li, Vladimir G. Romanov +1
The problem of imaging of a moving target is formulated as a Coefficient Inverse Problem for a hyperbolic equation with its coefficient depending on all three spatial variables and…
Normalized solutions for a class of fractional Choquard equations with mixed nonlinearities
Shaoxiong Chen, Zhipeng Yang, Xi Zhang
In this paper we study the following fractional Choquard equation with mixed nonlinearities: \[ \left\{ \begin{array}{l} (-Δ)^s u = λu + α\left( I_μ* |u|^q \right) |u|^{q-2} u + \l…
Normalized Solutions and Semiclassical Concentration for Upper-Critical Fractional Choquard Equations
Yergen Aikyn, Yongpeng Chen, Michael Ruzhansky +1
We study a fractional Choquard equation with an upper-critical Hartree term, an -supercritical Hartree perturbation, and a semiclassical potential under a prescribed -mas…
Multiplicity of bound states for a class of nonlinear Dirac equations on generalized star graphs with potentials
Guangze Gu, Ziwei Li, Michael Ruzhansky +1
In this paper we investigate the existence and multiplicity of bound states for a class of nonlinear Dirac equations on a generalized star graph \(\mathcal{G}\): \[ -ic\,σ_1\,\part…
Nonrelativistic limit of bound-state solutions for nonlinear Dirac equation on noncompact quantum graphs
Guangze Gu, Michael Ruzhansky, Guoyan Wei +1
In this paper, we investigate the nonrelativistic limit and qualitative properties of bound-state solutions for the nonlinear Dirac equation (NLDE) defined on noncompact quantum gr…
Existence and concentration of multiple solutions for the fractional logarithmic Schrödinger-Poisson system via the penalization method
Jiao Luo, Zhipeng Yang
We study positive solutions of the fractional logarithmic Schrödinger-Poisson system \[ \begin{cases} \varepsilon^{2α}(-Δ)^αu+V(x)u+ϕu=u\log u^2+|u|^{q-2}u, & \text{in } \mathbb{R}…
A low-rank solver for the Stokes-Darcy model with random hydraulic conductivity and Beavers-Joseph condition
Yujun Zhu, Yulan Ning, Zhipeng Yang +2
This paper proposes, analyzes, and demonstrates an efficient low-rank solver for the stochastic Stokes-Darcy interface model with a random hydraulic conductivity both in the porous…
On the existence of normalized solutions to a class of fractional Choquard equation with potentials
Yongpeng Chen, Zhipeng Yang, Jianjun Zhang
This paper investigates the existence of normalized solutions to the nonlinear fractional Choquard equation: $$ (-Δ)^s u+V(x) u=λu+f(x)\left(I_α*\left(f|u|^q\right)\right)|u|^{q-2}…
Bound states of nonlinear Dirac equations on periodic quantum graphs
Zhipeng Yang, Ling Zhu
We study nonlinear Dirac equations (NLDE) on periodic quantum graphs endowed with Kirchhoff-type vertex conditions. Our main goal is to establish existence and multiplicity of boun…
Critical fractional Kirchhoff problems: Uniqueness and Nondegeneracy
Zhipeng Yang, Yuanyang Yu
In this paper, we consider the following critical fractional Kirchhoff equation \begin{equation*} \Big(a+b{\int_{\mathbb{R}^{N}}}|(-Δ)^{\frac{s}{2}}u|^2dx\Big)(-Δ)^su=|u|^{2^*_s-2}…
Convexification With the Viscocity Term for Electrical Impedance Tomography
Michael V. Klibanov, Jingzhi Li, Zhipeng Yang
A version of the globally convergent convexification numerical method is constructed for the problem of Electrical Impedance Tomography in the 2D case. An important element of this…