Abstract. This paper presents the multiscale analysis and computation for parabolic equations with rapidly oscillating coefficients in general domains. The major contributions of this study are twofold. First, we define the boundary layer solution and the convergence rate with ε1/2 for the multiscale asymptotic solutions in general domains. Secondly, a highly accurate computational algorithm is...

In a perforated domain, we consider reaction-diffusion system with rapidly oscillating terms in the equations and boundary conditions. No Lipschitz condition is imposed, so uniqueness of solution to corresponding initial-boundary value problem not guaranteed. We prove that trajectory attractors weakly converge homogenized systems strange term (potential).

INTRODUCTION The aim of this research was to describe nomograms of brainstem auditory evoked potentials, oscillating stimulation of the vestibular organs and ultrastructural research methodology of a spiral organ of guinea-pigs. MATERIALS AND METHODS For the experimental purposes 60 guinea-pigs of both sexes, weight 250-300 grams, were used as research materials. After general anesthesia with...

In recent years, there has been renewed interest in problems of diffraction and radiation of ocean waves around structures, in relation to “green” power generation by Oscillating Water Column (OWC) devices. In this paper we present a first-order analytical solution for the diffraction of ocean waves around a hollow cylindrical shell structure suspended in an ocean of finite depth. By revisiting...

To solve boundary value problems of stationary heat distribution in composite materials, one has to solve partial di¤erential equations with rapidly oscillating coe¢cients. These equations are in general impossible to solve numerically by standard methods. Instead, one wants to ...nd constant, effective conductivities and solve the corresponding boundary value problem to get an approximate solu...

A dispersion-managed optical system with stepwise periodic variation of dispersion is studied in a strong dispersion map limit in the framework of the path-averaged Gabitov-Turitsyn equation. The soliton solution is obtained by analytical and numerical iteration of the path-averaged equation. An efficient numerical algorithm for finding a DM soliton shape is developed. The envelope of soliton o...

We introduce a time-dependent perturbation method to calculate the number of created particles in a 1D cavity with an oscillating wall of the frequency Ω. This method makes it easy to find the dominant part of the solution which results from the parametric resonance. The maximal number of particles are created at the mode frequency Ω/2. Using the Floquet theory, we discuss the long-time behavio...

An analytic solution of the flow of a third-grade fluid on a porous plate is constructed. The porous plate is executing oscillations in its own plane with superimposed injection or suction. An increasing or decreasing velocity amplitude of the oscillating porous plate is also examined. It is also shown that in case of third-grade fluid, a combination of suction/injection and decreasing/increasi...

In this paper we establish new homogenization results for stochastic linear hyperbolic equations with periodically oscillating coefficients. We first use the multiple expansion method to drive the homogenized problem. Next we use the two scale convergence method and Prokhorov’s and Skorokhod’s probabilistic compactness results. We prove that the sequence of solutions of the original problem con...

The current voltage characteristic of the narrow superconducting channel is investigated by direct numerical integration of the time-dependent Ginzburg Landau equations. We have demonstrated that the steps in the current voltage characteristic correspond to a number of di erent bifurcation points of the time-dependent Ginzburg Landau equations. We have analytically estimated the period and the ...