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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：A structure-preserving parametric finite element method (PFEM) for geometric PDEs and applications
几何偏微分方程 结构保持 参数有限元
2023/4/17
In this talk, I begin with a review of different geometric flows (PDEs) including mean curvature (curve shortening) flow,surface diffusion flow, Willmore flow, etc., which arise from materials science...
2018非线性偏微分方程和几何分析研讨会（Geometric and Nonlinear Partial Differential Equations Conference）
2018 非线性偏微分方程和几何分析 研讨会
2017/12/20
This conference will demonstrate and strengthen connections between geometric analysis and nonlinear partial differential equations. We focus on new advances in several related themes, which include v...
An improved geometric inequality via vanishing moments, with applications to singular Liouville equations
Geometric PDEs Variational Methods Min-max Schemes
2012/6/14
We consider a class of singular Liouville equations on compact surfaces motivated by the study of Electroweak and Self-Dual Chern-Simons theories, the Gaussian curvature prescription with conical sing...
The Algebro-Geometric Initial Value Problem for the Ruijsenaars-Toda Hierarchy and Quasi-Periodic Solutions
Ruijsenaars-Toda hierarchy complex-valued algebro-geometric solutions hyperelliptic curve Dubrovin-type equation Baker-Akhiezer vector
2012/4/27
We provide a detailed treatment of Ruijsenaars-Toda (RT) hierarchy with special emphasis on its the theta function representation of all algebro-geometric solutions. The basic tools involve hyperellip...
The global solutions of algebro-geometric type for Degasperis-Procesi hierarchy
The global solutions of algebro-geometric type Degasperis-Procesi hierarchy Exactly Solvable and Integrable Systems
2012/4/26
Though completely integrable Camassa-Holm (CH) equation and Degasperis-Procesi (DP) equation are cast in the same peakon family, they possess the second- and third-order Lax operators, respectively. F...
Barrier methods for critical exponent problems in geometric analysis and mathematical physics
Nonlinear elliptic equations geometric analysis Yamabe problem general relativity
2011/8/23
Abstract: We consider the design and analysis of numerical methods for approximating positive solutions to nonlinear geometric elliptic partial differential equations containing critical exponents. Th...
A geometric approach to integrability of Abel differential equations
Abel equation Lie systems Jacobi multiplier
2011/1/20
A geometric approach is used to study the Abel first order differential equation of the first kind. The approach is based on the recently developed theory of quasi-Lie systems which allows us to chara...
Carleman estimates for elliptic operators with jumps at an interface: Anisotropic case and sharp geometric conditions
Carleman estimate elliptic operator non-smooth coecient quasimode
2011/2/21
We consider a second-order selfadjoint elliptic operator with an anisotropic di usion matrix having a jump across a smooth hypersurface. We prove the existence of a weight-function such that a Carlema...
Geometric methods for nonlinear many-body quantum systems
Geometric methods nonlinear many-body quantum systems
2010/12/6
Geometric techniques have played an important role in the seventies, for the study of the spectrum of many-body Schr¨odinger operators. In this paper we provide a formalism which also allows to study ...
Geometric shape of invariant manifolds for a class of stochastic partial differential equations
Stochastic partial differential equation invariant manifolds geometric shape
2010/12/6
Invariant manifolds play an important role in the study of the qualitative dynamical behaviors for nonlinear stochastic partial differential equations. However, the geometric shape of
these manifolds...
A geometric criterion for the non-uniform hyperbolicity of the Kontsevich--Zorich cocycle
geometric criterion non-uniform hyperbolicity Kontsevich--Zorich cocycle
2010/12/10
We prove a geometric criterion on a SL(2,R)-invariant ergodic probability measure on the moduli space of holomorphic abelian differentials on Riemann surfaces for the non-uniform hyperbolicity of the ...