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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...
Very high frequency deep radio sounding systems for ice thickness measurements are practically the only useful apparatuses for large scale radar flight surveys in polar regions. The morphology of the ...
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&...

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