Related papers: Sivashinsky equation in a rectangular domain
We study the existence and uniqueness of a solution to a linear stationary convection-diffusion equation stated in an infinite cylinder, Neumann boundary condition being imposed on the boundary. We assume that the cylinder is a junction of…
It is shown that solutions of the Neumann problem for the Poisson equation in an arbitrary convex $n$-dimensional domain are uniformly Lipschitz. Applications of this result to some aspects of regularity of solutions to the Neumann problem…
A review of solutions of solid-state diffusion problems in infinite and semi-infinite bodies is presented. Based on the identified solutions for the semi-infinite body a two-step diffusion problem is discussed in detail with the first step…
Initial-boundary value problems for the $n$-dimensional ($n$ is a natural number from the interval [2,7]) Kuramoto-Sivashinsky equation posed on smooth bounded domains in $\mathbb{R}^n$ were considered. The existence and uniqueness of…
Thermodiffusive instabilities can have a leading order effect on flame propagation for lean premixed hydrogen flames. Many simulation studies have been performed to study this effect, but almost exclusively in two-dimensional (2D) or domain…
Steady propagation of premixed flames in straight channels is studied numerically using the on-shell approach. A first numerical algorithm for solving the system of nonlinear integro-differential on-shell equations is presented. It is based…
A model consisting of a mixed Kuramoto - Sivashinsky - KdV equation, linearly coupled to an extra linear dissipative equation, is proposed. The model applies to the description of surface waves on multilayered liquid films. The extra…
The influence of the small scale ``cellular'' structure of premixed flames on their evolution at larger scales is investigated. A procedure of the space-time averaging of the flow variables over flame cells is introduced. It is proved that…
A theory of flame propagation in curved channels is developed within the framework of the on-shell description of premixed flames. Employing the Green function appropriate to the given channel geometry, an implicit integral representation…
The problem of premixed flame propagation in wide horizontal tubes is revisited. Employing the on-shell description of flames with arbitrary gas expansion, a nonlinear second-order differential equation for the front position of steady…
We report numerical simulations of one-dimensional cellular solutions of the stabilized Kuramoto-Sivashinsky equation. This equation offers a range of generic behavior in pattern-forming instabilities of moving interfaces, such as a host of…
We revisit the Near Equidiffusional Flames (NEF) model introduced by Matkowsky and Sivashinsky in 1979 and consider a simplified, quasi-steady version of it. This simplification allows, near the planar front, an explicit derivation of the…
Understanding the propagation dynamics of premixed flames in confined spaces is important for fire safety in gas pipelines and for optimizing modern internal combustion engines. In sufficiently long channels, premixed flames routinely…
Global well-posedness of the initial-boundary value problem for the stochastic Kuramoto-Sivashinsky equation in a bounded domain $D$ with a multiplicative noise is studied. It is shown that under suitable sufficient conditions, for any…
We study in this article the stochastic Zakharov-Kuznetsov equation driven by a multiplicative noise. We establish, in space dimensions two and three the global existence of martingale solutions, and in space dimension two the global…
The problem of burning of high-velocity gas streams in channels is revisited. Previous treatments of this issue are found to be incomplete. It is shown that despite relative smallness of the transversal gas velocity, it plays crucial role…
We consider the Dirichlet problem for a class of semilinear equations on two dimensional convex domains. We give a sufficient condition for the solution to be concave. Our condition uses comparison with ellipses, and is motivated by an idea…
We first briefly recall the basic mechanisms controlling the hydrodynamic and thermo-diffusive stability of planar laminar premixed flames, and give the state of the theoretical analysis. We then describe some novel experiments to observe…
Different approaches to the nonlinear dynamics of premixed flames exist in the literature: equations based on developments in a gas ex- pansion parameter, weak nonlinearity approximation, potential model equation in a coordinate-free form.…
Nonlinear non-stationary equation describing evolution of weakly curved premixed flames with arbitrary gas expansion, subject to the Landau-Darrieus instability, is derived. The new equation respects all the conservation laws to be…