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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Analytic smoothing effect of a class of ultra-parabolic equations
一类超抛物型方程 解析 光滑效应
2023/11/29
We study a class of ultra-parabolic equations, it is a high order degenerate parabolic operators of Hormander type, so it is strongly degenerate, but we prove that this class operators possesses the a...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Liouville theorems for superlinear parabolic problems
超线性 抛物线问题 刘维尔定理
2023/4/21
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...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars： Liouville theorems for superlinear parabolic problems
超线性 抛物线问题 刘维尔定理
2023/4/23
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...
ELLIPTIC RECONSTRUCTION AND A POSTERIORI ERROR ESTIMATES FOR PARABOLIC PROBLEMS
A posteriori error estimators fi nite elements semidiscrete parabolic problems
2015/12/11
It is known that the energy technique for a posteriori error analysis
of finite element discretizations of parabolic problems yields suboptimal rates
in the norm L1(0; T;L2
(Ω)): In thi...
A POSTERIORI ERROR ANALYSIS FOR PARABOLIC VARIATIONAL INEQUALITIES
variational inequality American option pricing
2015/12/11
Motivated by the pricing of American options for baskets we consider a parabolic variational inequality in a bounded polyhedral domain Ω ⊂ Rd with a continuous piecewise smooth obstacle.
...
STRONGLY ESSENTIAL FLOWS ON IRREDUCIBLE PARABOLIC GEOMETRIES
STRONGLY ESSENTIAL FLOWS GEOMETRIES
2015/10/14
We study the local geometry of irreducible parabolic geometries admitting
strongly essential
ows; these are
ows by local automorphisms with higher-order xed
points. We prove several new rigidit...
ESSENTIAL KILLING FIELDS OF PARABOLIC GEOMETRIES: PROJECTIVE AND CONFORMAL STRUCTURES
PARABOLIC GEOMETRIES PROJECTIVE
2015/10/14
We use the general theory developed in our article [1]
in the setting of parabolic geometries to reprove known results on
special in nitesimal automorphisms of projective and conformal
geometries.
We study vector elds generating a local
ow by automorphisms of a parabolic geometry with higher order xed points.
We develop general tools extending the techniques of [1], [2], and
[3], and we a...
Nonlinear Stochastic Perturbations of Dynamical Systems and Quasi-linear Parabolic PDE’s with a Small Parameter
Quasi linear parabolic equations parameters quasi linear initial boundary value
2015/9/28
In this paper we describe the asymptotic behavior, in the exponential time scale, of solutions to quasi-linear parabolic equations with a small parameter at the second order term and the long time beh...
Averaging principle for quasi-linear parabolic PDE’s and related diffusion processes
Quasi linear disturbance two dimensional flow parabola and small parameter
2015/9/28
Quasi-linear perturbations of a two-dimensional flow with a first integral and the corresponding parabolic PDE’s with a small parameter at the second order derivatives are considered in th...
DIFFERENTIAL HARNACK ESTIMATES FOR PARABOLIC EQUATIONS
PARABOLIC EQUATIONS DIFFERENTIAL HARNACK
2015/8/17
Let (M, g(t)) be a solution to the Ricci flow on a closed Riemannian
manifold. In this paper, we prove differential Harnack inequalities for positive
solutions of nonlinear parabolic equ...
The Harnack inequality for second-order parabolic equations with divergence-free drifts of low regularity
Harnack inequality second-order parabolic equations divergence-free drifts low regularity
2015/7/14
We establish the Harnack inequality for advection-diffusion equations with divergencefree drifts of low regularity.While our previous work [IKR] considered the elliptic case, here we treat the more ch...
Sobolev spaces Hγ(M), γ ∈ R, M ⊂ Rd
M-bounded
Def If n ∈ N, then Hn - all generalized functions with derivatives up to
n-th order belong to L2(M); kuk 2Hn = P |α | ≤n R
M
|Dαu| 2dx
Initial-irregular oblique derivative problem for nonlinear parabolic equations of second order in multiply connected domains
Initial-irregular oblique derivative problem nonlinear parabolic equa-tions multiply connected domains
2014/9/26
n this article, we discuss that an initial-irregular oblique derivative problem for non-linear uniformly parabolic complex equation of second order
A0
u
zˉ z −Re[Quzz+A1
u
z
]−A2
u&...
Initial-oblique derivative boundary value problem for nonlinear parabolic equations of second order
Initial-oblique derivative problem, nonlinear parabolic complex equations multiply connected domains
2014/9/26
In this article, we discuss that an initial-oblique derivative boundary value
problem for nonlinear uniformly parabolic complex equation of second order
A0
u
z1z¡Re[Quzz+A1
u
z
]¡
^
...