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We discuss a class of two-parameters coupled Kirchhoff-type fractional differential equations. Two differentiated methods are used to prove the existence of two solutions to the equation. The fundamen...
We focus on the study of t-stabilities on a triangulated category in the sense of Gorodentsev, Kuleshov and Rudakov. We give an equivalent description for the nest t-stabilities on certain triangulate...
对于接触Hamilton-Jacobi方程H(x,Du(x),u(x))=0,H满足Tonelli条件,讨论弱KAM解的结构以及解的Lyapunov稳定性。此外,在单位圆情形时,去掉H关于u 单调性的假设,把条件放宽到对它在一个时间周期内积分平均值的要求,研究它与解的稳定性之间的关系,不稳定时证明不同周期非平凡周期解的存在性,稳定时给出收敛速度。
本报告讨论Hamilton系统辛算法的KAM稳定性,给出辛算法应用于近可积系统时不变环面的存在性证明和数值逼近结果。具体地,近可积系统用辛算法离散化,假设系统的可积部分满足Ruessmann非退化条件,当时间步长足够小且Hamilton函数足够光滑时,离散系统存在不变环面,它们在相应空间中占据一个大测度Cantor集。进而假设系统的可积部分满足Kolmogorov非退化条件,则在Hausdorff...
We use the nonlinear steepest descent for Riemann-Hilbert problems to compute the long-time asymptotics of the solutions to the sine-Gordon equation whose initial condition belongs to some weighted So...
We study positive solutions of the Yamabe equation with isolated singularity and prove the existence of solutions with prescribed asymptotic expansions near singular points and an arbitrarily high ord...
We first consider positive classical solutions to a semilinear heat equation and discuss the associated Liouville-type theorems and their consequences on a priori estimates of solutions (in particular...
In this talk we will review some recent results on space-time finite and boundary element methods for the wave equation. As a first model problem we consider the inhomogeneous wave equation with zero ...
In this talk, we discuss the global stability of the Minkowski spacetime in the wave coordinates system for the massive Einstein-Vlasov system. In particular, compared with previous results by Lindbla...
We consider the existence, uniqueness and nonlinear stability of the travelling wave solution of the Navier-Stokes-Poisson system with density-dependent viscosity for ions. Firstly, we derive a system...
In this talk, we talk about the proof of the O(2)-symmetry of 3D steady gradient solitons. The proof consists of four parts: the asymptotic analysis at infinity, the symmetry improvement theorem, the ...
We consider the genealogical tree of a stationary continuous state branching process with immigration. For a sub-critical stable branching mechanism, we consider the genealogical tree of the extant po...
In his pioneering work in 1860, Riemann proposed the Riemann problem and solved it for isentropic gas in terms of shocks and rarefaction waves. It eventually became the foundation of the theory of one...
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...
This talk will survey some results for the two- or three-space dimensional compressible Euler equations. We shall present non-uniqueness results of weak entropy solutions using convex integration and ...

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