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Convection-diffusion problem are the base for continuum mechanics. The main features of these problems are associated with an indefinite operator the problem. In this work we construct unconditionally stable scheme for non-stationary…
Diffusion flame streets, observed in non-premixed micro-combustion devices, align parallel to a shear flow. They are observed to occur in mixtures with high Lewis number ($Le$) fuels, provided that the flow Reynolds number, or the Peclet…
We give an explicit formula for the change of speed of pushed and bistable fronts of the reaction diffusion equation when a small cutoff is applied at the unstable or metastable equilibrium point. The results are valid for arbitrary…
Three-dimensional turbulence simulations are used to show that the turbulent root mean square velocity is an upper bound of the speed of turbulent diffusion. There is a close analogy to magnetic diffusion where the maximum diffusion speed…
We use stable maps, and their stable lifts to the Semple bundle variety of second-order curvilinear data, to calculate certain characteristic numbers for rational plane curves. These characteristic numbers involve first-order (tangency) and…
We consider the stability of a system of equations which are a singular perturbation of the incompressible rigid-plastic flow equations used to model granular flow. A linear stability analysis shows that solutions of these equations are…
This paper is devoted to reaction-diffusion equations with bistable nonlinearities depending periodically on time. These equations admit two linearly stable states. However, the reaction terms may not be bistable at every time. These may…
A solution to a given equation is structurally stable if it suffers only an infinitesimal change when the equation (not the solution) is perturbed infinitesimally. We have found that structural stability can be used as a velocity selection…
We study the stochastic diffusive limit of a kinetic radiative transfer equation, which is non-linear, involving a small parameter and perturbed by a smooth random term. Under an appropriate scaling for the small parameter, using a…
We derive general properties of anomalous diffusion and nonexponential relaxation from the theory of tempered \alpha-stable processes. Its most important application is to overcome the infinite-moment difficulty for the \alpha-stable random…
The statistical analysis of covariance matrices occurs in many important applications, e.g. in diffusion tensor imaging and longitudinal data analysis. We consider the situation where it is of interest to estimate an average covariance…
Observations and magnetohydrodynamic simulations of solar and stellar atmospheres reveal an intermittent behavior or steep gradients in physical parameters, such as magnetic field, temperature, and bulk velocities. The numerical solution of…
We consider a reaction-diffusion equation in narrow random channels. We approximate the generalized solution to this equation by the corresponding one on a random graph. By making use of large deviation analysis we study the asymptotic wave…
Dispersion-managed solitons are reviewed within a Gaussian variational approximation and an integral evolution model. In the normal regime of the dispersion map (when the averaged path dispersion is negative), there are two solitons of…
We numerically address the stability analysis of linear age-structured population models with nonlocal diffusion, which arise naturally in describing dynamics of infectious diseases. Compared to Laplace diffusion, models with nonlocal…
The study of pattern-forming instabilities in reaction-diffusion systems on growing or otherwise time-dependent domains arises in a variety of settings, including applications in developmental biology, spatial ecology, and experimental…
We will give some regularity results about fractional diffusion-wave equations.
Weighted averaged finite difference methods for solving fractional diffusion equations are discussed and different formulae of the discretization of the Riemann-Liouville derivative are considered. The stability analysis of the different…
In this paper, we show that the quasi-one-dimensional flow of an ideal inviscid fluid in a corrugated pipe is parametrically unstable in certain frequency bands. First-order perturbation theory is used to analyze the stability of the flow,…
The basic stationary buoyant flow in a vertical annular porous passage induced by a boundary temperature difference is investigated. The vertical cylindrical boundaries are considered both isothermal and permeable to external fluid…