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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Critical Allard regularity in dimension two and its application
二维中临界 阿拉德规律性 欧几里得空间
2023/5/5
The classical Allard regularity says, a rectifiable varifold in the unit ball of the Euclidean space passing through the original point with volume density close to 1 and generalized mean curvature sm...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On the classification of entire solutions to the critical p-Laplace equation
临界 p-拉普拉斯方程 整个解 分类
2023/5/9
In this talk, we will focus on the classification of positive solutions to the critical p-Laplace equation. It is well known that such issue is crucial in many applications such as a priori estimates,...
EXCURSIONS AND OCCUPATION TIMES OF CRITICAL EXCITED RANDOM WALKS
EXCURSIONS AND OCCUPATION TIMES EXCITED RANDOM WALKS
2015/9/29
We consider excited random walks (ERWs) on integers in i.i.d. environments with a bounded number of excitations per site. The emphasis is primarily on
the critical case for the transition between rec...
PARAMETER CHOICE FOR FAMILIES OF MAPS WITH MANY CRITICAL POINTS
PARAMETER CHOICE MAPS WITH MANY CRITICAL POINTS
2015/9/25
We consider families of smooth one-dimensional maps with several critical points and outline the main ideas of the construction in the parameter space that allows to get infinite Markov Partitions and...
The critical group of an abelian network is a finite abelian group that governs the behavior of the network on large inputs. It generalizes the sandpile group of a graph. We show that the critical gro...
The divisible sandpile starts with i.i.d. random variables (“masses”) at the vertices of an infinite, vertex-transitive graph, and redistributes mass by a local toppling rule in an attempt to make all...
BIOMIXING BY CHEMOTAXIS AND EFFICIENCY OF BIOLOGICAL REACTIONS:THE CRITICAL REACTION CASE
CHEMOTAXIS EFFICIENCY BIOLOGICAL REACTIONS CRITICAL REACTION CASE
2015/7/14
Many phenomena in biology involve both reactions and chemotaxis. These processes can clearly influence each other, and chemotaxis can play an important role in sustaining and speeding up the reaction....
Random Attractors for Stochastic Wave Equations with Critical Exponents on Rn
Stochastic Wave Equations Random Attractors
2015/4/3
Outline
• Stochastic wave equations on Rn.
• Random attractors theory.
• Random absorbing sets for wave equations.
• Pullback asymptotic compactness.
• Existence of ...
Standing waves with critical frequency for nonlinear Schrodinger equations
Standing waves critical frequency nonlinear Schrodinger equations
2015/4/3
Standing waves with critical frequency for nonlinear Schrodinger equations.
Shilnikov Lemma for a normally hyperbolic critical manifold of a Hamiltonian system
Shilnikov Lemma normally hyperbolic critical manifold Hamiltonian system
2015/3/18
Shilnikov Lemma for a normally hyperbolic critical manifold of a Hamiltonian system.
Asymptotics of the Fredholm determinant corresponding to the first bulk critical universality class in random matrix models
Integrable operators Riemann-Hilbert approach Deift-Zhou method asymptotical analysis of Fredholm determinants
2015/1/19
We study the one-parameter family of determinants $det(I-\gamma K_{PII}),\gamma\in\mathbb{R}$ of an integrable Fredholm operator $K_{PII}$ acting on the interval $(-s,s)$ whose kernel is constructed o...
On the critical dissipative quasi-geostrophic equation
the critical dissipative quasi-geostrophic equation
2014/4/4
The 2D quasi-geostrophic (QG) equation is a two dimensional model of the 3D incompressible Euler equations. When dissipation is included in the model then solutions always exist if the dissipation's w...
GLOBAL REGULARITY FOR A MODIFIED CRITICAL DISSIPATIVE QUASI-GEOSTROPHIC EQUATION
GLOBAL REGULARITY A MODIFIED CRITICAL DISSIPATIVE QUASI-GEOSTROPHIC EQUATION
2014/4/3
with κ > 0, α ∈ (0,1] and θ0 ∈ L2(R2). We remark that the extra Λα−1 is introduced in order to make the scaling invariance of this system similar to the scaling invariance of the critical quasi-...
We prove the existence of a compact global attractor for the dynamics of the forced critical surface quasi-geostrophic equation (SQG) and prove that it has finite fractal (box-counting) dimensio...
A Critical Exponent of Fujita Type for a Nonlinear Reaction-Di usion System on Riemannian Manifold
critical exponent reaction-di usion system Riemannian manifold.
2018/4/19
In this paper, we study the global existence and nonexistence of positive solutions to the
following nonlinear reaction-di usion system
8>>>>>>>>>>>><
>>>>>>>>>>>>:
ut u = W(x)vp + S(x...