Related papers: Remarks on parabolic Kolmogorov operator
In the homogenization of monotone parabolic partial differential equations with oscillations in both the space and time variables the gradients converges only weakly in $L^p$. In the present paper we construct a family of correctors, such…
In this paper we show that the rotational Smagorinsky model for turbulent flows, can be put, for a wide range of parameters in the setting of Bochner pseudo-monotone evolution equations. This allows to prove existence of weak solutions a)…
We define various higher-order Markov properties for stochastic processes $(X(t))_{t\in \mathbb{T}}$, indexed by an interval $\mathbb{T} \subseteq \mathbb{R}$ and taking values in a real and separable Hilbert space $U$. We furthermore…
The paper introduces a very simple and fast computation method for high-dimensional integrals to solve high-dimensional Kolmogorov partial differential equations (PDEs). The new machine learning-based method is obtained by solving a…
The present paper aims to generalize the Schauder estimate for a class of higher-order hypo-elliptic operators. The results in the present paper apply to parabolic equations of higher order and, for example, operators like…
We consider a family of second-order parabolic operators $\partial_t+\mathcal{L}_\varepsilon$ in divergence form with rapidly oscillating, time-dependent and almost-periodic coefficients. We establish uniform interior and boundary H\"older…
We describe the architecture of an evolving algebra partial evaluator, a program which specializes an evolving algebra with respect to a portion of its input. We discuss the particular analysis, specialization, and optimization techniques…
This paper first proves the existence, uniqueness and regularity of the solution to a class of linear backward parabolic equations on Carnot tori, namely the periodic linear parabolic equation on Carnot groups. Such groups are…
The purpose of this paper is to investigate the well-posedness of several linear and nonlinear equations with a parabolic forward-backward structure, and to highlight the similarities and differences between them. The epitomal linear…
Using an original method, we find the algebra of generalized symmetries of a remarkable (1+2)-dimensional ultraparabolic Fokker-Planck equation, which is also called the Kolmogorov equation and is singled out within the entire class of…
This work is on a user-friendly reduced basis method for solving a family of parametric PDEs by preconditioned Krylov subspace methods including the conjugate gradient method, generalized minimum residual method, and bi-conjugate gradient…
We propose a new stabilised finite element method for the classical Kolmogorov equation. The latter serves as a basic model problem for large classes of kinetic-type equations and, crucially, is characterised by degenerate diffusion. The…
We obtain solutions of the nonlinear degenerate parabolic equation \[ \frac{\partial \rho}{\partial t} = {div} \Big\{\rho \nabla c^\star [ \nabla (F^\prime(\rho)+V) ] \Big\} \] as a steepest descent of an energy with respect to a convex…
We sample a velocity field that has an inertial spectrum and a skewness that matches experimental data. In particular, we compute a self-consistent correction to the Kolmogorov exponent and find that for our model it is zero. We find that…
We show that any stochastically monotone Feller semigroup on R can be extended by a consistent family of order-preserving Feller semigroups on the successive powers of R. We exhibit a specific such family, which is uniquely characterized by…
We suggest a modification of the estimate for weighted Sobolev norms of solutions of parabolic equations such that the matrix of the higher order coefficients is included into the weight for the gradient. More precisely, we found the upper…
The problem of computing differential constraints for a family of evolution PDEs is discussed from a constructive point of view. A new method, based on the existence of generalized characteristics for evolution vector fields, is proposed in…
We carry on the investigation started in [2] about the regularity of weak solutions to the strongly degenerate parabolic equation \[ u_{t}-\mathrm{div}\left[(\vert Du\vert-1)_{+}^{p-1}\frac{Du}{\vert…
The main aim of this article is to establish an $L_p$-theory for elliptic operators on manifolds with singularities. The particular class of differential operators discussed herein may exhibit degenerate or singular behavior near the…
Extended systems governed by partial differential equations can, under suitable conditions, be approximated by means of sets of ordinary differential equations for global quantities capturing the essential features of the systems dynamics.…