asymptotic solution

Wave concept of motion in mathematical models of the dynamics of two-dimensional media studying

The methodology of the studying of dynamic processes in two-dimensional systems by mathematical models containing nonlinear equation of Klein-Gordon was developed. The methodology contains such underlying: the concept of the motion wave theory; the single - frequency fluctuations principle in nonlinear systems; the asymptotic methods of nonlinear mechanics. The aggregate content allowed describing the dynamic process for the undisturbed (linear) analogue of the mathematical model of movement.

Asymptotic solutions of soliton type of the Korteweg–de Vries equation with variable coefficients and singular perturbation

The paper deals with the singularly perturbed Korteweg–de Vries equation with variable coefficients.  The equation describes wave processes in various inhomogeneous media with variable characteristics and small dispersion.  We consider the general algorithm of construction of asymptotic solutions of soliton type to the equation and present its approximate solutions of this type.  We analyze properties of the constructed asymptotic solution depending on a small parameter.  The results are demonstrated by the examples of the studied equation.  We show that for an adequate description of quali

Spatial modeling of multicomponent pollution removal for liquid treatment under identification of mass transfer coefficient

A generalized spatial mathematical model of the multicomponent pollutant removal for a liquid treatment is proposed. Under the assumption of domination of convective processes over diffusive ones, the model considers an inverse influence of the determining factor (pollution concentration in water and sludge) on the media characteristics (porosity, diffusion) and takes into account the specified additional condition (overridden condition) for estimation of the unknown mass transfer coefficient of a small value.

Investigation of the solution’s properties to problem of electromagnetic scattering on a set of small inclusions

The problem of scattering of the electromagnetic (EM) waves by many small impedance bodies (particles), embedded in a homogeneous medium is studied. Physical properties of the particles are described by their boundary impedance. The boundary integral equation is obtained for the effective EM field in the limiting medium for the case if radius of particles tends to zero and number of particles tends to infinity by suitable rate. The medium, created by the embedding of the small particles, has new physical properties.

Identification of mass-transfer coefficient in spatial problem of filtration

A modeling problem of the process of liquid multi component decontamination by a spatial filter is considered, it takes into account the reverse influence of decisive factors (contamination concentrations of liquid and sediment) on characteristics (coefficient of porosity, diffusion) of the medium and gives us the possibility to determine small mass transfer coefficient under the conditions of prevailing of convective constituents over diffusive ones.