18 citations · 24 across the 12 of their papers we have counts for
12 papers
Boundary layers and vanishing diffusivity in run-and-tumble models
Dallas Albritton, Laurel Ohm, Timur Yastrzhembskiy
A notable feature of confined active matter systems is the tendency for motile particles to accumulate near solid boundaries. In various linear models with no-flux boundary conditi…
Asymptotic Stability for Relativistic Vlasov-Maxwell-Landau System in Bounded Domain
Hongjie Dong, Yan Guo, Timur Yastrzhembskiy
The control of plasma-wall interactions is crucial to fusion devices from both physical and mathematical perspectives. It is well known that a magnetic field satisfying the classic…
The Local-well-posedness of the relativistic Vlasov-Maxwell-Landau system with the specular reflection boundary condition
Hongjie Dong, Yan Guo, Zhimeng Ouyang +1
We prove the local-in-time well-posedness of the relativistic Vlasov-Maxwell-Landau system in a bounded domain with the specular reflection condition. Our result covers the cas…
Global Schauder estimates for kinetic Kolmogorov-Fokker-Planck equations
Hongjie Dong, Timur Yastrzhembskiy
We present global Schauder type estimates in all variables and unique solvability results in kinetic Hölder spaces for kinetic Kolmogorov-Fokker-Planck (KFP) equations. The leading…
Global estimates for kinetic Kolmogorov-Fokker-Planck equations in divergence form
Hongjie Dong, Timur Yastrzhembskiy
We present a priori estimates and unique solvability results in the mixed-norm Lebesgue spaces for kinetic Kolmogorov-Fokker-Planck (KFP) equation in divergence form. The leading c…
Kinetic Fokker-Planck and Landau Equations with Specular Reflection Boundary Condition
Hongjie Dong, Yan Guo, Timur Yastrzhembskiy
We establish existence of finite energy weak solutions to the kinetic Fokker-Planck equation and the linearized Landau equation near Maxwellian, in the presence of specular reflect…
Global estimates for kinetic Kolmogorov-Fokker-Planck equations in nondivergence form
Hongjie Dong, Timur Yastrzhembskiy
We study the degenerate Kolmogorov equations (also known as kinetic Fokker-Planck equations) in nondivergence form. The leading coefficients are merely measurable in a…
A note on the strong Feller property of diffusion processes
Timur Yastrzhembskiy
In this note we prove the strong Feller property of a strong Markov quasi diffusion process corresponding to an elliptic operator with merely bounded measurable coefficients. We al…
On the stability estimates for stochastic and deterministic difference equations and their application to SPDEs and PDEs
Timur Yastrzhembskiy
In this paper we develop the -theory of space-time stochastic difference equations which can be considered as a discrete counterpart of N.V. Krylov's -theory of stochasti…
Support theorem for an SPDE with multiplicative noise driven by a cylindrical Wiener process on the real line
Timur Yastrzhembskiy
We prove a Stroock-Varadhan's type support theorem for a stochastic partial differential equation (SPDE) on the real line with a noise term driven by a cylindrical Wiener process o…
Wong-Zakai approximation and support theorem for semilinear SPDEs with finite dimensional noise in the whole space
Timur Yastrzhembskiy
In this paper we consider the following stochastic partial differential equation (SPDE) in the whole space: $du (t, x) = [a^{i j} (t, x) D_{i j} u(t, x) + f(u, t, x)]\, dt + \sum_{…
On nonequivalence of regular boundary points for second-order elliptic operators
N. V. Krylov, Timur Yastrzhembskiy
In this paper we present examples of nondivergence form second order elliptic operators with continuous coefficients such that has an irregular boundary point that is regular f…