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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Functions of bounded variation and nonlocal functionals
有界 变差函数 非局部泛函
2023/11/29
In the past two decades, starting with the pioneering work of Bourgain, Brezis, and Mironescu, there has been widespread interest in characterizing Sobolev and BV (bounded variation) functions by mean...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Energy stability of exponential time differencing schemes for the nonlocal Cahn-Hilliard equation
非局部 Cahn-Hilliard方程 指数时间 差分方案 能量稳定性
2023/4/24
In this talk, we consider a class of exponential time differencing (ETD) schemes for solving the nonlocal Cahn-Hilliard equation. We first use the Fourier collocation method to discretize the space do...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Nonlocal Filtration Equations on the Heisenberg group
海森堡群 非局部 滤波方程
2023/4/28
Since the work by Caffarelli-Chan-Silvestre-Vasseur, integro-differential equations naturally arise from models in physics, engineering, and finance, attracting an increasing level of interest. They a...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars： Nonlocal Filtration Equations on the Heisenberg group
海森堡群 非局部 滤波方程
2023/5/4
Since the work by Caffarelli-Chan-Silvestre-Vasseur, integro-differential equations naturally arise from models in physics, engineering, and finance, attracting an increasing level of interest. They a...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：ENERGY, POINTWISE, AND FREE BOUNDARY APPROXIMATION OF THE OBSTACLE PROBLEM FOR NONLOCAL OPERATORS
非局部 算子障碍物 自由边界 近似
2023/4/28
We consider the obstacle problem for a nonlocal elliptic operator, like the integral fractional Laplacian of order $s \in (0,1)$. We derive regularity results in weighted Sobolev spaces, where the wei...
Wave-like solutions for nonlocal reaction-diffusion equations: a toy model
Traveling wave Wavetrains Nonlocal elliptic equations
2015/7/14
Traveling waves for the nonlocal Fisher Equation can exhibit much more complex behaviours than for the usual Fisher equation. A striking numerical observation is that a traveling wave with minimal spe...
On the nonlocal Fisher-KPP equation:steady states,spreading speed and global bounds
nonlocal Fisher-KPP equation steady states spreading speed global bounds
2015/7/14
We consider the Fisher-KPP equation with a non-local interaction term. We establish a condition on the interaction that allows for existence of non-constant periodic solutions,and prove uniform upper ...
NONLINEAR MAXIMUM PRINCIPLES FOR DISSIPATIVE LINEAR NONLOCAL OPERATORS AND APPLICATIONS
NONLINEAR MAXIMUM PRINCIPLES DISSIPATIVE LINEAR NONLOCAL OPERATORS APPLICATIONS
2014/4/3
We obtain a family of nonlinear maximum principles for linear dissipative nonlocal operators,that are general, robust, and versatile. We use these nonlinear bounds to provide transparent proofs of glo...
Analysis Of A One-Dimensional Nonlocal Quasicontinuum Method
Quasicontinuum method ghost force geometrically consistent scheme
2012/8/10
The accuracy of the quasicontinuum method is analyzed using a series of models
with increasing complexity. It is demonstrated that the existence of the ghost force may lead to large
errors. It is al...
On dyadic nonlocal Schr鰀inger equations with Besov initial data
Schrodinger equation Besov spaces Haar bases Nonlocal derivatives
2012/6/21
In this paper we characterize a dyadic type Besov space as an adequate setting to solve the Schr\"{o}dinger-Dirac type equation $i\tfrac{\partial u}{\partial t}=D^{\beta}u$ with $u(x,0)=u^0$ pointwise...
Controllability of Semilinear Evolution Inclusions with Nonlocal Conditions
Controllability fixed point semilinear evolution inclusions
2011/11/4
In this paper, the controllability of semilinear evolution inclusions with nonlocal conditions in Banach spaces is investigated when the multivalued map has nonconvex values. The approach used here is...
Global and trajectory attractors for a nonlocal Cahn-Hilliard-Navier-Stokes system
Navier-Stokes equations nonlocal Cahn-Hilliard equations incompressible binary fluids global attractors
2011/9/23
Abstract: The Cahn-Hilliard-Navier-Stokes system is based on a well-known diffuse interface model and describes the evolution of an incompressible isothermal mixture of binary fluids. A nonlocal varia...
Local and nonlocal pressure Hessian effects in real and synthetic fluid turbulence
pressure Hessian effects real synthetic fluid turbulence
2011/7/7
The Lagrangian dynamics of the velocity gradient tensor A in isotropic and homogeneous turbulence depend on the joint action of the self-streching term and the pressure Hessian. Existing closures for ...
Nonlocal wave turbulence in the Charney-Hasegawa-Mima equation: a short review
Nonlocal wave turbulence short review
2010/12/28
Rossby wave turbulence, as modelled by the Charney-Hasegawa-Mima (CHM) equation, is nonlo-
cal in scale. As a result, the formal stationary Kolmogorov-Zakharov solutions of the Rossby wave kinetic eq...
Blow-up for a degenerate and singular parabolic system with nonlocal sources and absorptions
Degenerate and singular parabolic system blow up blow-up set
2010/11/1
This paper deals with the blow-up properties of the solution to the degenerate and singular parabolic system with nonlocal sources, absorptions and homogeneous Dirichlet boundary conditions. The exist...