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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Strichartz estimates for wave equations with a potential in non-trapping exterior domains
斯特里查茨估计 非陷阱外域 波动方程
2023/4/14
Consider the linear wave equations with a potential outside a compact set with a non-trapping boundary condition. Assuming that the potential satisfies an appropriate decreasing condition and that zer...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Some estimates on an exterior Steklov eigenvalue problem
外部 斯特克洛夫特征值 估计
2023/5/9
In this talk we will discuss a Steklov eigenvalue problem on an exterior Euclidean domain. We will present sharp lower and upper bounds for its first eigenvalue under various conditions on the domain....
Self-similar asymptotics of solutions to the Navier-Stokes system in two dimensional exterior domain
Self-similar asymptotics the Navier-Stokes system two dimensional exterior domain Analysis of PDEs
2011/9/1
Abstract: We consider the 2D incompressible Navier-Stokes equations with Dirichlet boundary condition in the exterior of one obstacle. Assuming that the circulation at infinity of the velocity is suff...
Asymptotic description of solutions of the exterior Navier Stokes problem in a half space
Asymptotic description exterior Navier Stokes problem a half space
2011/8/25
Abstract: We consider the problem of a body moving within an incompressible fluid at constant speed parallel to a wall, in an otherwise unbounded domain. This situation is modeled by the incompressibl...
On the polygonal diameter of the interior, resp. exterior, of a simple closed polygon in the plane
Jordan-Brouwer theorem Jordan exterior (interior) Jordan’s curve theorem
2011/2/21
We give a tight upper bound on the polygonal diameter of the interior, resp. exterior, of a simple n-gon, n ≥ 3, in the plane as a function of n, and describe an n-gon (n ≥ 3) for which both upper bou...
Semilinear elliptic inequalities in the exterior of a compact set
Semilinear elliptic inequalities compact set
2010/11/24
We study the semilinear elliptic inequality $-\Delta u\geq\varphi(\delta_K(x))f(u)$ in $R^N\setminus K,$ where $\varphi, f$ are non-negative and continuous functions, $K\subset R^N$ $(N\geq 2)$ is a ...
Lower bound of the lifespan of solutions to semilinear wave equations in an exterior domain
Lower bound lifespan of solutions semilinear wave equations
2010/11/30
We consider the Cauchy-Dirichlet problem for semilinear wave equations in a three space dimensional domain exterior to a bounded and non-trapping obstacle. We obtain a detailed estimate for the lower ...
Exterior cloaking with active sources in two dimensional acoustics
Active cloaking Acoustic waves Helmholtz equation Green’s formula
2010/12/3
We cloak a region from a known incident wave by surrounding the region with three or more devices that cancel out the field in the cloaked region without significantly radiating waves. Since very litt...
Let O be the ring of integers of a non-Archimedean local eld and a xed uniformizer of O. We establish three main results.
Flows driven by a combination of source/sink part 1: Exterior creeping flows
Flows driven combination source sink
2010/9/15
In this paper, the two-dimensional creeping flows outside a circular cylinder induced by source/sink with various boundary conditions is studied.
Eigenvalue Asymptotics of the Even-Dimensional Exterior Landau-Neumann Hamiltonian
Eigenvalue Asymptotics magnetic field Landau-Neumann Hamiltonian
2009/9/4
We study the Schrödinger operator with a constant magnetic field in the exterior of a compact domain in ℝ2d, d≥1. The spectrum of this operator consists of clusters of eigenvalues around th...
Flow generated by stokeslets. Part 1. Exterior creeping flows
Fourier expansion creeping flow cylinder stokeslet
2010/9/14
Steady two-dimensional flows induced by line stokeslets in the presence of an infinitely long circular cylinder with no-slip boundary condition are examined. The stokeslets consider here located outsi...
In this paper, we prove that there is a natural equivalence between the category ${\scr F}_1(x)$ of Koszul modules of complexity $1$ with filtration of given cyclic modules as the factor modules of an...
A numerical method combining the approaches of C.I. Goldstein and L.-A. Ying is used for the simulation in three-dimensional magnetostatics related to an exterior problem in magnetic induction. Recent...
Positive Solutions of a Class of Quasilinear Elliptic Equations in Two-dimensional Exterior Domains
Positive solution Quasilinear elliptic equation Exterior domains
2007/12/12
Sufficient conditions for the existence of positive solutions to a class of quasilinear elliptic equations in two-dimensional exterior domains are given.