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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Convergence in probability from moderate interacting SDE system to degenerate Keller-Segel systema
中度相互作用 SDE系统 凯勒-西格尔系统 概率收敛性
2023/4/13
In this talk I will present one of our recent work in rigorous derivation of the degenerate parabolic-elliptic Keller-Segel system. We establish the classical solution theory of the degenerate parabol...
Anomalous diffusion limit for kinetic equations with degenerate collision frequency
Anomalous diffusion limit kinetic equations degenerate collision frequency
2015/10/15
This paper is devoted to hydrodynamic limits for collisional linear kinetic equations. It is a classical result that under certain conditions on the collision operator, the long time/small mean free p...
C^{1,1} regularity for degenerate elliptic obstacle problems in mathematical finance
American-style option degenerate elliptic differential operator degenerate diffusion process free boundary problem Heston stochastic volatility process
2012/6/21
The Heston stochastic volatility process is a degenerate diffusion process where the degeneracy in the diffusion coefficient is proportional to the square root of the distance to the boundary of the h...
Stability of bound states of Hamiltonian PDEs in the degenerate cases
Hamiltonian PDEs degenerate cases Analysis of PDEs
2011/9/14
Abstract: We consider a Hamiltonian systems which is invariant under a one-parameter unitary group. We give a criterion for the stability and instability of bound states for the degenerate case. We ap...
Unique continuation and approximate controllability for a degenerate parabolic equation
degenerate parabolic equations unique continuation approximate controllability local Carleman estimate
2011/9/13
Abstract: This paper studies unique continuation for weakly degenerate parabolic equations in one space dimension. A new Carleman estimate of local type is obtained to deduce that all solutions that v...
q-damped Oscillator and degenerate roots of constant coefficients q-difference ODE
q-damped Oscillator degenerate roots coefficients q-difference ODE
2011/9/5
Abstract: The classical model of q-damped oscillator is introduced and solved in terms of Jackson q-exponential function for three different cases, under-damped, over-damped and the critical one. It i...
A nonlinear degenerate elliptic problem with W^{1,1}_0 solutions
nonlinear degenerate elliptic problem Analysis of PDEs
2011/8/26
Abstract: We study a nonlinear equation with an elliptic operator having degenerate coercivity. We prove the existence of a unique W^{1,1}_0 distributional solution under suitable summability assumpti...
Derivative Formula and Applications for Degenerate Diffusion Semigroups
Derivative formula Gradient estimate Harnack inequality Stochastic differential equation
2011/8/22
Abstract: By using the Malliavin calculus and solving a control problem, Bismut type derivative formulae are established for a class of degenerate diffusion semigroups with non-linear drifts. As appli...
Homogenizations of integro-differential equations with L{é}vy operators with asymmetric and degenerate densities
Homogenizations of integro-differential equations L{é}vy operators asymmetric degenerate densities
2011/1/21
We consider periodic homogenization problems for the L´evy operators with asymmetric L´evy densities. The formal asymptotic expansion used for the -stable (symmetric) L´evy operator...
Multiplicity and regularity of periodic solutions for a class of degenerate semilinear wave equations
Multiplicity regularity of periodic solutions class of degenerate semilinear wave equations
2011/2/28
We prove the existence of infinitely many classical periodic solutions for a class of degenerate semilinear wave equations:utt − uxx + |u|s−1u = f(x, t),for all s > 1. In particular we pro...
Blow-up for a degenerate and singular parabolic system with nonlocal sources and absorptions
Degenerate and singular parabolic system blow up blow-up set
2010/11/1
This paper deals with the blow-up properties of the solution to the degenerate and singular parabolic system with nonlocal sources, absorptions and homogeneous Dirichlet boundary conditions. The exist...
Formal matched asymptotics for degenerate Ricci flow neckpinches
Formal matched asymptotics Ricci flow neckpinches
2010/11/24
Gu and Zhu have shown that Type-II Ricci flow singularities develop from nongeneric rotationally symmetric Riemannian metrics on $S^m$, for all $m\geq 3$. In this paper, we describe and provide plaus...
Classification of non-degenerate projective varieties with non-zero prolongation and application to target rigidity
non-degenerate projective varieties non-zero prolongation
2010/11/24
The prolongation g^{(k)} of a linear Lie algebra g \subset gl(V) plays an important role in the study of symmetries of G-structures. Cartan and Kobayashi-Nagano have given a complete classification o...
Degenerate diffusion with a drift potential: a viscosity solutions approach, joint work with I. C. Kim, truncated version
drift potential viscosity solutions approach
2010/11/23
This is a truncated version of the paper "Degenerate diffusion with a drift potential: a viscosity solutions approach", co-authored with I. C. Kim. The purpose of this version is to withdraw the claim...
A finite volume method on general meshes for a degenerate parabolic convection-reaction-diffusion equation
parabolic convection-reaction-diffusion equation math
2010/11/23
We propose a finite volume method on general meshes for the discretization of a degenerate parabolic convection-reaction-diffusion equation. Equations of this type arise in many contexts, such as the ...