Related papers: Instabilities in a combustion model with two free …
We study solutions to a one-phase singular perturbation problem that arises in combustion theory and that formally approximates the classical one-phase free boundary problem. We introduce a natural density condition on the transition layers…
The interface separating a liquid from its vapor phase is diffuse: the composition varies continuously from one phase to the other over a finite length. Recent experiments on dynamic jamming fronts in two dimensions [Waitukaitis et al.,…
This work deals with a scalar nonlinear neutral delay differential equation issued from the study of wave propagation. A critical value of the coefficients is considered, where only few results are known. The difficulty follows from the…
This paper continues the investigation of Du and Lou (J. European Math Soc, to appear), where the long-time behavior of positive solutions to a nonlinear diffusion equation of the form $u_t=u_{xx}+f(u)$ for $x$ over a varying interval…
In order to study the stability of mode-I fracture, we consider a crack moving along the centerline of a very wide strip and compute its steady-state response to a small, spatially periodic shear stress. We find that, in the presence of…
We investigate a coordinate-free model of flame fronts introduced by Frankel and Sivashinsky; this model has a parameter $\alpha$ which relates to how unstable the front might be. We first prove short-time well-posedness of the…
We discuss the front propagation in ferroelectric chiral smectics (SmC*) subjected to electric and magnetic fields applied parallel to smectic layers. The reversal of the electric field induces the motion of domain walls or fronts that…
Fuel-lean hydrogen combustion systems hold significant potential for low pollutant emissions, but are also susceptible to intrinsic combustion instabilities. While most research on these instabilities has focused on flames without wall…
In this paper, we focus on the existence of propagation fronts, solutions to non-local dispersion reaction models. Our aim is to provide a unified proof of this existence in a very broad framework using simple real analysis tools. In…
We provide a mathematical analysis of a thermo-diffusive combustion model of lean spray flames, for which we prove the existence of travelling waves. In the high activation energy singular limit we show the existence of two distinct…
Intrinsic instabilities of laminar premixed flames play an important role in the dynamics of hydrogen combustion and in the development of predictive models for reacting flows. However, determining their dispersion relations typically…
Preferential diffusion plays a critical role in the evolution of lean premixed hydrogen flames, influencing flame surface corrugation and overall flame behavior. Simulating such flames with tabulated chemistry (TC) methods remains…
The main goal of this paper is to understand finer properties of the effective burning velocity from a combustion model introduced by Majda and Souganidis [19]. Motivated by results in [4] and applications in turbulent combustion, we show…
A new diffuse interface model for a two-phase flow of two incompressible fluids with different densities is introduced using methods from rational continuum mechanics. The model fulfills local and global dissipation inequalities and is…
We study a two-component reaction-diffusion system in which one of the reaction terms becomes singularly large. Assuming that the initial data are nonnegative and mutually segregated, we prove that the solution converges to that of the heat…
In this paper we formulate and analyze an elementary model for the propagation of advancing autoignition fronts in reactive co-flow fuel/oxidizer jets injected into an aqueous environment at high pressure. This work is motivated by the…
The problem of non-perturbative description of stationary flames with arbitrary gas expansion is considered. On the basis of the Thomson circulation theorem an implicit integral of the flow equations is constructed. With the help of this…
The dynamic initiation of sliding at planar interfaces between deformable and rigid solids is studied with particular focus on the speed of the slip front. Recent experimental results showed a close relation between this speed and the local…
Direct interactions between the flow field and the chemical reaction in premixed flames occur when the reaction zone thickness is comparable to, or greater than flow length scales. To study such interactions, a laminar model is considered…
Pattern formation in reaction-diffusion systems where the diffusion terms correspond to a Sturm-Liouville problem are studied. These correspond to a problem where the diffusion coefficient depends on the spatial variable: $\nabla \cdot…