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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Long-time asymptotics of soliton equations via the nonlinear steepest descent method
非线性 最速下降法 孤立子方程 长时间渐近性
2023/11/13
Based on the matrix block technique, the Deift-Zhou nonlinear steepest descent method is developed in order to study the asymptotic analysis of solutions of some nonlinear evolution equations associat...
A polynomial-time algorithm for determining quadratic Lyapunov functions for nonlinear systems
Nonlinear systems quadratic lyapunov function and convex programming function
2015/8/12
We consider nonlinear systems dx/dt=f(x(t)) where Df(x(t)) is known to lie in the convex hull of L n times n matrices A_1,ldots,A_L. For such systems, quadratic Lyapunov functions can be determined us...
The Boltzmann equation, Besov spaces, and optimal time decay rates in the whole space
Kinetic Theory Boltzmann equation long-range interaction non cutoff soft potentials hard potentials fractional derivatives
2012/6/6
We prove that $k$-th order derivatives of perturbative classical solutions to the hard and soft potential Boltzmann equation (without the angular cut-off assumption) in the whole space, $\threed_x$ wi...
Local-in-space estimates near initial time for weak solutions of the Navier-Stokes equations and forward self-similar solutions
Local-in-space estimates initial time weak solutions of the Navier-Stokes equations forward self-similar solutions Analysis of PDEs
2012/4/18
We show that the classical Cauchy problem for the incompressible 3d Navier-Stokes equations with $(-1)$-homogeneous initial data has a global scale-invariant solution which is smooth for positive time...
Long-time dynamics of the parabolic $p$-Laplacian equation
p-Laplacian equation attractors Long-time dynamics
2012/2/29
In this paper, we study the long-time behaviour of solutions of Cauchy problem for the parabolic $p$-Laplacian equation with variable coefficients. Under mild conditions on the coefficient of the prin...
On the long-time behavior of some mathematical models for nematic liquid crystals
liquid crystals Navier-Stokes system omega-limit set
2011/9/21
Abstract: A model describing the evolution of a liquid crystal substance in the nematic phase is investigated in terms of two basic state variables: the {\it velocity field} $\bu$ and the {\it directo...
Global existence of small amplitude solution to nonlinear system of wave and Klein-Gordon equations in four space-time dimensions
Global existence nonlinear system wave and Klein-Gordon equations four space-time dimensions
2011/9/14
Abstract: In this article one will develop a so-called hyperboloidal foliation method, which is an energy method based on a foliation of space-time into hyperboloidal hypersurfaces. This method permit...
Periodic long-time behaviour for an approximate model of nematic polymers
Periodic long-time behaviour nematic polymers Analysis of PDEs
2011/9/14
Abstract: We study the long-time behaviour of a nonlinear Fokker-Planck equation, which models the evolution of rigid polymers in a given flow, after a closure approximation. The aim of this work is t...
Time relaxation of a phase-field model with entropy balance
phase-field model entropy balance Analysis of PDEs
2011/9/14
Abstract: We deal with a system of two coupled differential equations, describing the evolution of a first order phase transition. In particular, we have two non-linear parabolic equations: the first ...
On the well-posedness of weakly hyperbolic equations with time dependent coefficients
Hyperbolic equations Gevrey spaces ultradistributions Analysis of PDEs
2011/9/5
Abstract: In this paper we analyse the Gevrey well-posedness of the Cauchy problem for weakly hyperbolic equations of general form with time-dependent coefficients. The results involve the order of lo...
The enclosure method for inverse obstacle scattering problems with dynamical data over a finite time interval II. Obstacles with a dissipative boundary or finite refractive index and back-scattering data
enclosure method inverse obstacle scattering problem inverse backscattering obstacle wave equation dissipative boundary condition
2011/9/5
Abstract: In this paper a wave is generated by an initial data whose support is localized at the outside of unknown obstacles and observed in a limited time on a known closed surface or the same posit...
Green's function and large time behavior of the Navier-Stokes-Maxwell system
Navier-Stokes-Maxwell system dissipation Green’s function asymptotic stability
2011/9/1
Abstract: In this paper, we are concerned with the system of the compressible Navier-Stokes equations coupled with the Maxwell equations through the Lorentz force in three space dimensions. The asympt...
A large time asymptotics for the solution of the Cauchy problem for the Novikov-Veselov equation at negative energy with non-singular scattering data
large time asymptotics the Cauchy problem non-singular scattering data Analysis of PDEs
2011/8/26
Abstract: In the present paper we are concerned with the Novikov--Veselov equation at negative energy, i.e. with the $(2 + 1)$--dimensional analog of the KdV equation integrable by the method of inver...
Global-in-time existence of perturbations around travelling-waves
nonlinear and nonlocal conservation law fractional anti-diffusive operator Duhamel formulation travelling-wave global-in-time existence
2011/8/22
Abstract: We investigate a fractional diffusion/anti-diffusion equation proposed by Andrew C. Fowler to describe the dynamics of sand dunes sheared by a fluid flow. In this paper, we prove the global-...
Constructing elliptic curve isogenies in quantum subexponential time
Constructing elliptic curve isogenies quantum subexponential time
2011/3/3
Given two elliptic curves over a finite field having the same cardinality and endomorphism
ring, it is known that the curves admit an isogeny between them, but finding such an isogeny is believed to ...