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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...
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...
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
]¡
^
...
Parabolic equations with dynamical boundary conditions and source terms on interfaces
parabolic equation quasilinear parabolic problem mixed boundary condition dynamical boundary condition maximal parabolic Lp-regularity
2012/6/19
We consider parabolic equations with mixed boundary conditions and domain inhomogeneities supported on a lower dimensional hypersurface, enforcing a jump in the conormal derivative. Only minimal regul...
Carleman Estimate for Stochastic Parabolic Equations and Inverse Stochastic Parabolic Problems
Stochastic parabolic equations Carleman estimate conditional stability inverse source problem
2011/9/22
Abstract: In this paper, we establish a global Carleman estimate for stochastic parabolic equations. Based on this estimate, we solve two inverse problems for stochastic parabolic equations. One is co...
An O(k2+kh2+h2) Accurate Two-level Implicit Cubic Spline Method for One Space Dimensional Quasi-linear Parabolic Equations
Quasi-Linear Parabolic Equation, Implicit Method, Cubic Spline Approximation, Diffusion-Convection Equation, Singular Equation, Burgers’ Equation, Reynolds Number
2013/1/30
In this piece of work, using three spatial grid points, we discuss a new two-level implicit cubic spline method of O(k2 + kh2 + h4) for the solution of quasi-linear parabolic equation , 0< x <1, t > 0...
Smooth Contractive Embeddings and Application to Feynman Formula for Parabolic Equations on Smooth Bounded Domains
Smooth contractive extension operator elliptic differential operator
2011/1/18
We prove two assumptions made in an article by Ya.A. Butko, M. Grothaus,O.G. Smolyanov concerning the existence of a strongly continuous operator semi-group solving a Cauchy-Dirichlet problem for an e...
Quasilinear Parabolic Equations and the Ricci Flow on Manifolds with Boundary
Quasilinear Parabolic Equations Ricci Manifolds with Boundary
2011/1/21
The first part of the paper discusses a second-order quasilinear parabolic equation in a vector bundle over a compact manifold M with boundary @M. We establish a short-time existence theorem for this ...
Treatment of Incompatible Initial and Boundary Data for Parabolic Equations in Higher Dimension
Incompatible Initial Boundary Data
2010/11/24
A new method is proposed to improve the numeri- cal simulation of time dependent problems when the initial and boundary data are not compatible. Unlike earlier methods limited to space dimension one,...
The Harnack inequality and related properties for solutions to elliptic and parabolic equations with divergence-free lower-order coefficients
The Harnack inequality related properties elliptic
2010/11/15
We discuss the problem how "bad" may be lower-order coefficients in elliptic and parabolic second order equations to ensure some qualitative properties of solution such as strong maximum principle, H...
Existence of solutions and separation from singularities for a class of fourth order degenerate parabolic equations
degenerate fourth-order parabolic equation separation from singularities long-time behavior
2010/12/8
A nonlinear parabolic equation of the fourth order is analyzed. The equation is characterized
by a mobility coefficient that degenerates at 0. Existence of at least one weak solution is proved by usi...
Capacitary estimates of solutions of semilinear parabolic equations
Heat equation singularities Borel measures Bessel capacities Wiener type test
2010/12/13
We prove that any positive solution of ∂tu − u + uq = 0 (q > 1) in RN × (0,∞) with
initial trace (F, 0), where F is a closed subset of RN can be represented, up to two universal
multipl...
Degenerate homogeneous parabolic equations associated with the infinity-Laplacian
Degenerate homogeneous parabolic equations infinity-Laplacian
2010/12/8
We prove existence and uniqueness of viscosity solutions to the degenerate parabolic problem ut = h 1u where h 1 is the h-homogeneous operator associated with the infinity-Laplacian, h 1u = |Du|h&#...