Related papers: Instabilities in a combustion model with two free …
The present paper is devoted to the investigation of various properties of transition fronts in nonlocal equations in heterogeneous media of ignition type, whose existence has been established by the authors of the present paper in a…
We present the first realistic 3D simulations of flame front instabilities during type I X-ray bursts. The unperturbed front is characterised by the balance between the pressure gradient and the Coriolis force of a spinning neutron star…
We prove the existence and uniqueness, up to a shift in time, of curved traveling fronts for a reaction-advection-diffusion equation with a combustion-type nonlinearity. The advection is through a shear flow $q$. This analyzes, for…
The system under study is a reaction-diffusion equation in a horizontal strip, coupled to a diffusion equation on its upper boundary via an exchange condition of the Robin type. This class of models was introduced by H. Berestycki, L. Rossi…
When the steady states at infinity become unstable through a pattern forming bifurcation, a travelling wave may bifurcate into a modulated front which is time-periodic in a moving frame. This scenario has been studied by B.Sandstede and…
A newly developed sharp interface model describes crack propagation by a phase transition process. We solve this free boundary problem numerically and obtain steady state solutions with a self-consistently selected propagation velocity and…
Propagation of premixed flames having thick reaction zones in rapidly-varying, small-scale, zero-mean, spatio-temporal periodic flows is considered. Techniques of large activation energy asymptotics and homogenization theory are used to…
The response and nonconserved dynamics of a two-phase interface in the presence of a temperature gradient oriented normally to the interface are considered. Two types of boundary conditions on the order parameter are considered, and the…
We study the existence and stability of propagating fronts in Meinhardt's multivariable reaction-diffusion model of branching in one spatial dimension. We identify a saddle-node-infinite-period (SNIPER) bifurcation of fronts that leads to…
In this paper we put forward a viral propagation model with nonlinear infection rate and free boundaries and investigate the dynamical properties. This model is composed of two ordinary differential equations and one partial differential…
We study the interfaces arising in the two-dimensional Ising model at critical temperature, without magnetic field. We show that in the presence of free boundary conditions between plus and minus spins, the scaling limit of these interfaces…
We study the free boundary in an unstable parabolic problem arising from a model in combustion. We consider the physical situation in which the heat advances and prove that the free boundary is a $C^{1,\alpha/2}$ hypersurface.
For certain values of the wave speed parameter, evolution equations for the temperature of a region of fuel admit traveling wave solutions describing fire fronts. We consider such a system in the form of a nonlinear reaction-diffusion…
Planar flames are intrinsically unstable in open domains due to the thermal expansion across the burning front--the Landau-Darrieus instability. This instability leads to wrinkling and growth of the flame surface, and corresponding…
We study the spectral stability of travelling and stationary front and pulse solutions in a class of degenerate reaction-diffusion systems. We characterise the essential spectrum of the linearised operator in full generality and identify…
The morphology of flame fronts propagating in reactive systems comprised of randomly positioned, point-like sources is studied. The solution of the temperature field and the initiation of new sources is implemented using the superposition…
We study interfacial behavior of a lamellar (stripe) phase coexisting with a disordered phase. Systematic analytical expansions are obtained for the interfacial profile in the vicinity of a tricritical point. They are characterized by a…
The structure of flame filaments resulting from chaotic mixing within a combustion reaction is considered. The transverse profile of the filaments is investigated numerically and analytically based on a one-dimensional model that represents…
We study nonlinear diffusion problems of the form $u_t=u_{xx}+f(u)$ with free boundaries. Such problems may be used to describe the spreading of a biological or chemical species, with the free boundary representing the expanding front. For…
The two-way interaction between the unsteady flame heat release rate and acoustic waves can lead to combustion instability within combustors. To understand and quantify the flame response to oncoming acoustic waves, previous studies have…