7 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…
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…