Related papers: Asymptotic Analysis in a Gas-Solid Combustion Mode…
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…
We consider the Cauchy problem for plate equations with rotational inertia and frictional damping terms. We will derive asymptotic profiles of the solution in L^2-sense as time goes to infinity in the case when the initial data have high…
We consider time-dependent convection-diffusion problems with high P\'eclet number of order $\mathcal{O}(\varepsilon^{-1})$ in thin three-dimensional graph-like networks consisting of cylinders that are interconnected by small domains…
In this paper we consider the long time asymptotics of a linear version of the Smoluchowski equation which describes the evolution of a tagged particle moving at constant speed in a random distribution of fixed particles. The volumes $v$ of…
It has been suggested recently that growth and division of a protocell could be modeled by a chemically active droplet with simple chemical reactions driven by an external fuel supply. This model is called the continuum model. Indeed it's…
We study the long-time behavior of localized solutions to linear or semilinear parabolic equations in the whole space $\mathbb{R}^n$, where $n \ge 2$, assuming that the diffusion matrix depends on the space variable $x$ and has a finite…
In this section, we consider the heat equation on a plate with thickness h > 0 being heated by a heat source on upper and lower faces of the plate. We obtain an asymptotic profile of the solution as the thickness h > 0 approaches to zero.
We study the asymptotic behavior of the kinetic free-transport equation enclosed in a regular domain, on which no symmetry assumption is made, with Cercignani-Lampis boundary condition. We give the first proof of existence of a steady state…
We consider the dynamics and kinetic roughening of interfaces embedded in uniformly random media near percolation treshold. In particular, we study simple discrete ``forest fire'' lattice models through Monte Carlo simulations in two and…
There is scientific and industrial interest in understanding how geologic faults respond to transient sources of fluid. Natural and artificial sources can elevate pore fluid pressure on the fault frictional interface, which may induce slip.…
A generalized Neumann solution for the two-phase fractional Lam\'e--Clapeyron--Stefan problem for a semi--infinite material with constant initial temperature and a particular heat flux condition at the fixed face is obtained, when a…
Using pole decompositions as starting points, the one parameter (-1 =< c < 1) nonlocal and nonlinear Zhdanov-Trubnikov (ZT) equation for the steady shapes of premixed gaseous flames is studied in the large-wrinkle limit. The singular…
We consider a free boundary problem for the heat equation with a given non-negative external heat source. On the free boundary, we impose the zero Dirichlet condition and the fixed normal derivative so that heat escapes from the boundary.…
As lean premixed combustion systems are more susceptible to combustion instabilities than non-premixed systems, there is an increasing demand for improved numerical design tools that can predict the occurrence of combustion instabilities…
We study how the propagation speed of interfaces in the Allen-Cahn phase field model for phase transformations in solids consisting of the elasticity equations and the Allen-Cahn equation depends on two parameters of the model. The two…
This paper is mainly concerned with the free boundary problem for an approximate model (for example, arising from the study of sonoluminescence) of a gas bubble of finite mass enclosed within a bounded incompressible viscous liquid,…
Phase field models for two-phase flow with a surfactant soluble in possibly both fluids are derived from balance equations and an energy inequality so that thermodynamic consistency is guaranteed. Via a formal asymptotic analysis, they are…
We derive a formula that simplifies the original asymptotic iteration method formulation to find the energy eigenvalues for the analytically solvable cases. We then show that there is a connection between the asymptotic iteration and the…
A recent paper [Phys. Plasmas 20, 032304 (2013)] considered the forced linear Vlasov equation as a model for the quasi-steady state of a single stable plasma wavenumber interacting with a bath of turbulent fluctuations. This approach gives…
Under specific experimental circumstances, sputter erosion on semiconductor materials exhibits highly ordered hexagonal dot-like nanostructures. In a recent attempt to theoretically understand this pattern forming process, Facsko et al.…