38 citations · 71 across the 9 of their papers we have counts for
14 papers
Hydrodynamics of a particle model in contact with stochastic reservoirs
Pasha Tkachov
We consider an exclusion process with finite-range interactions in the microscopic interval . The process is coupled with the simple symmetric exclusion processes in the int…
On stability of traveling wave solutions for integro-differential equations related to branching Markov processes
Pasha Tkachov
The aim of this paper is to prove stability of traveling waves for integro-differential equations connected with branching Markov processes. In other words, the limiting law of the…
Spatial growth processes with long range dispersion: microscopics, mesoscopics, and discrepancy in spread rate
Viktor Bezborodov, Luca Di Persio, Tyll Krueger +1
We consider the speed of propagation of a {continuous-time continuous-space} branching random walk with the additional restriction that the birth rate at any spatial point cannot e…
Pattern formation in the doubly-nonlocal Fisher-KPP equation
Christian Kuehn, Pasha Tkachov
We study the existence, bifurcations, and stability of stationary solutions for the doubly-nonlocal Fisher-KPP equation. We prove using Lyapunov-Schmidt reduction that under suitab…
An Ikehara-type theorem for functions convergent to zero
Dmitri Finkelshtein, Pasha Tkachov
We prove an analogue of the Ikehara theorem for positive non-increasing functions convergent to zero, generalising the results postulated in Diekmann, Kaper (1978, Nonlinear Anal.…
Doubly nonlocal Fisher-KPP equation: Front propagation
Dmitri Finkelshtein, Yuri Kondratiev, Pasha Tkachov
We study propagation over of the solution to a nonlocal nonlinear equation with anisotropic kernels, which can be interpretted as a doubly nonlocal reaction-diffusio…
Doubly nonlocal Fisher-KPP equation: Speeds and uniqueness of traveling waves
Dmitri Finkelshtein, Yuri Kondratiev, Pasha Tkachov
We study traveling waves for a reaction-diffusion equation with nonlocal anisotropic diffusion and a linear combination of local and nonlocal monostable-type reactions. We describe…
Doubly nonlocal Fisher-KPP equation: Existence and properties of traveling waves
Dmitri Finkelshtein, Yuri Kondratiev, Pasha Tkachov
We consider a reaction-diffusion equation with nonlocal anisotropic diffusion and a linear combination of local and nonlocal monostable-type reactions in a space of bounded functio…
Accelerated nonlocal nonsymmetric dispersion for monostable equations on the real line
Dmitri Finkelshtein, Pasha Tkachov
We consider the accelerated propagation of solutions to equations with a nonlocal linear dispersion on the real line and monostable nonlinearities (both local or nonlocal, however,…
Kesten's bound for sub-exponential densities on the real line and its multi-dimensional analogues
Dmitri Finkelshtein, Pasha Tkachov
We study the tail asymptotic of sub-exponential probability densities on the real line. Namely, we show that the n-fold convolution of a sub-exponential probability density on the…
Global stability in a nonlocal reaction-diffusion equation
Dmitri Finkelshtein, Yuri Kondratiev, Stanislav Molchanov +1
We study stability of stationary solutions for a class of non-local semilinear parabolic equations. To this end, we prove the Feynman--Kac formula for a Lévy processes with time-de…
The hair-trigger effect for a class of nonlocal nonlinear equations
Dmitri Finkelshtein, Pasha Tkachov
We prove the hair-trigger effect for a class of nonlocal nonlinear evolution equations on which have only two constant stationary solutions, and . The effec…
Accelerated front propagation for monostable equations with nonlocal diffusion: Multidimensional case
Dmitri Finkelshtein, Yuri Kondratiev, Pasha Tkachov
We describe acceleration of the front propagation for solutions to a class of monostable nonlinear equations with a nonlocal diffusion in , . We show that the…
Traveling waves and long-time behavior in a doubly nonlocal Fisher-KPP equation
Dmitri Finkelshtein, Yuri Kondratiev, Pasha Tkachov
We consider a Fisher-KPP-type equation, where both diffusion and nonlinear part are nonlocal, with anisotropic probability kernels. Under minimal conditions on the coefficients, we…