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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...
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...
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 ...
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&#...
Renormalized and Entropy Solutions for Nonlinear Parabolic Equations with Variable Exponents and L1 Data
Variable exponents Renormalized solutions Entropy solutions Exist- ence Uniqueness
2015/5/4
Abstract. In this paper we prove the existence and uniqueness of both renormalized solutions and entropy solutions for nonlinear parabolic equations with variable exponents and L 1 data. And moreover,...
H¨older continuity of the weak solutions for parabolic equations with the nonstandard growth condition
Boundedness H\
2007/12/12
In this paper, we investigate the interior regularity including the local boundedness and the interior H\"{o}lder continuity of weak solutions for parabolic equations of the $p(x,t)$-Laplacian type. W...
In this paper, we consider the numerical solution of quasi-parabolic equations of higher order by a spectral method, and propose a computational formula. We give an error estimate of approximate solut...