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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...
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...
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...
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...
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. ...
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...
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...
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...
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...
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...
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
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&...
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 ]¡ ^ ...

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