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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Rigidity of non-compact static domains in hyperbolic space via positive mass theorems
正质量定理 双曲空间 非紧致 静域刚性
2023/4/14
We single out a notion of staticity which applies to any domain in hyperbolic space whose boundary is a non-compact totally umbilical hypersurface. For (time-symmetric) initial data sets modeled at in...
Asymptotic behaviour of the doubly nonlinear equation $u_t=Δ_p u^m$ on bounded domains
doubly nonlinear equation slow di usion asymptotic behaviour self-similar solution convergence rates
2012/6/29
We study the homogeneous Dirichlet problem for the doubly nonlinear equation $u_t = \Delta_p u^m$, where $p>1,\ m>0$ posed in a bounded domain in $\mathbb{R}^N$ with homogeneous boundary conditions an...
Inversion of circular means and the wave equation on general planar domains
Inversion of circular equation general planar domains Analysis of PDEs
2012/6/25
We study the problem of recovering the initial data of the two dimensional wave equation from values of its solution on an arbitrarily shaped bounded domain $\Omega \subset \R^2$. As a main result we ...
Regularity of solutions to the polyharmonic equation in general domains
Regularity of solutions polyharmonic equation general domains Analysis of PDEs
2012/6/9
The present paper establishes boundedness of $[m-\frac n2+\frac 12]$ derivatives for the solutions to the polyharmonic equation of order $2m$ in arbitrary bounded open sets of $\RR^n$, $2\leq n\leq 2m...
On the existence of weak solutions to the three-dimensional steady compressible Navier-Stokes equations in bounded domains
Steady compressible Navier-Stokes equations existence for any γ > 1 weighted estimate bounded domains
2011/9/22
Abstract: We prove the existence of a weak solution to the three-dimensional steady compressible isentropic Navier-Stokes equations in bounded domains for any specific heat ratio \gamma > 1. Generally...
$H^2$ regularity for the $p(x)-$Laplacian in two-dimensional convex domains
Variable exponent spaces Elliptic Equations H2 regularity
2011/9/9
Abstract: In this paper we study the $H^2$ global regularity for solutions of the $p(x)-$Laplacian in two dimensional convex domains with Dirichlet boundary conditions. Here $p:\Omega \to [p_1,\infty)...
Dimension of attractors and invariant sets of damped wave equations in unbounded domains
damped wave equation invariant set attractor dimension
2011/9/5
Abstract: Under fairly general assumptions, we prove that every compact invariant set $\mathcal I$ of the semiflow generated by the semilinear damped wave equation u_{tt}+\alpha u_t+\beta(x)u-\Deltau ...
The 2D Euler equation on singular domains
2D Euler equation singular domains Analysis of PDEs
2011/8/29
Abstract: We establish the existence of global weak solutions of the 2D incompressible Euler equation, for a large class of non-smooth open sets. These open sets are the complements (in a simply conne...
Smooth Contractive Embeddings and Application to Feynman Formula for Parabolic Equations on Smooth Bounded Domains
Smooth contractive extension operator elliptic differential operator
2011/1/18
We prove two assumptions made in an article by Ya.A. Butko, M. Grothaus,O.G. Smolyanov concerning the existence of a strongly continuous operator semi-group solving a Cauchy-Dirichlet problem for an e...
Semiclassical limit for the nonlinear Klein Gordon equation in bounded domains
Klein Gordon Equation Semiclassical Limit Variational Methods Nonlinear Equations
2011/2/28
We are interested to the existence of standing waves for the nonlinear Klein Gordon equation "2 + W′( ) = 0 in a bounded domain D.
Sharp spectral stability estimates via the Lebesgue measure of domains for higher order elliptic operators
Elliptic equations Dirichlet and Neumann boundary conditions stability of eigenvalues
2011/2/25
We prove sharp stability estimates for the variation of the eigenvalues of non-negative self-adjoint elliptic operators of arbitrary even order upon variation of the open sets on which they are define...