11 citations · 33 across the 11 of their papers we have counts for
11 papers
Homogenization for the -Laplacian in a -dimensional ball perforated along the unit sphere: the critical case
Peter V. Gordon, Yuval Peres
We study a boundary value problem for the -Laplacian in the perforated domain , where and is the union of many small compact cavi…
Uniqueness of traveling fronts in premixed flames with stepwise ignition-temperature kinetics and fractional reaction order
Amanda Matson, Claude-Michel Brauner, Peter V. Gordon
In this paper, we consider a reaction-diffusion system describing the propagation of flames under the assumption of ignition-temperature kinetics and fractional reaction order. It…
A basic homogenization problem for the -Laplacian in perforated along a sphere: estimates
Peter V. Gordon, Fedor Nazarov, Yuval Peres
We consider a boundary value problem for the -Laplacian, posed in the exterior of small cavities that all have the same -capacity and are anchored to the unit sphere in $\mat…
Modeling of thermonuclear fusion flames : transition to detonation
Peter V. Gordon, Leonid Kagan, Gregory Sivashinsky
The paper is concerned with identification of the key mechanisms controlling deflagration-to-detonation transition in stellar medium. The issue of thermal runaway triggered by posi…
Gelfand-type problem for turbulent jets
Peter V. Gordon, Vitaly Moroz, Fedor Nazarov
We consider the model of auto-ignition (thermal explosion) of a free round reactive turbulent jet. This model falls into the general class of Gelfand-type problems and constitutes…
Strongly nonlinear asymptotic model of cellular instabilities in premixed flames with stepwise ignition temperature kinetics
Nathan Kilker, Dmitry Golovaty, Peter V. Gordon +2
In this paper we consider ignition-temperature, first-order reaction model of thermo-diffusive combustion that describes dynamics of thick flames arising in a theory of combustion…
Eventual self-similarity of solutions for the diffusion equation with nonlinear absorption and a point source
Peter V. Gordon, Cyrill B. Muratov
This paper is concerned with the transient dynamics described by the solutions of the reaction-diffusion equations in which the reaction term consists of a combination of a superli…
Gelfand type problem for two phase porous media
Peter V. Gordon, Vitaly Moroz
We consider a generalization of the Gelfand problem arising in Frank-Kamenetskii theory of thermal explosion. This generalization is a natural extension of the Gelfand problem to t…
Self-similarity and long-time behavior of solutions of the diffusion equation with nonlinear absorption and a boundary source
Peter V. Gordon, Cyrill B. Muratov
This paper deals with the long-time behavior of solutions of nonlinear reaction-diffusion equations describing formation of morphogen gradients, the concentration fields of molecul…
Multiplicity of supercritical fronts for reaction-diffusion equations in cylinders
P. V. Gordon, C. B. Muratov, M. Novaga
We study multiplicity of the supercritical traveling front solutions for scalar reaction-diffusion equations in infinite cylinders which invade a linearly unstable equilibrium. The…
Self-similar dynamics of morphogen gradients
Cyrill B. Muratov, Peter V. Gordon, Stanislav Y. Shvartsman
We discovered a class of self-similar solutions in nonlinear models describing the formation of morphogen gradients, the concentration fields of molecules acting as spatial regulat…