Nefedov, N. N.
Published in
Computational Mathematics and Mathematical Physics

AbstractThis work presents a review and analysis of modern asymptotic methods for analysis of singularly perturbed problems with interior and boundary layers. The central part of the work is a review of the work of the author and his colleagues and disciples. It highlights boundary and initial-boundary value problems for nonlinear elliptic and para...

Prokhorov, I. V. Yarovenko, I. P.
Published in
Computational Mathematics and Mathematical Physics

AbstractFor the nonstationary radiative transfer equation, the inverse problem of determining the attenuation coefficient from a known solution at the domain boundary is considered. The structure and the continuous properties of the solution to an initial-boundary value problem for the radiative transfer equation are studied. Under special assumpti...

Denisov, A. M.
Published in
Computational Mathematics and Mathematical Physics

AbstractFor the heat conduction equation with a singular perturbation corresponding to a small heat capacity or a small heat conductivity, inverse problems of determining the boundary or initial condition or the source term from additional information about the solution of the equation are considered. The possibility of using the expansion in a sma...

Vasil’ev, V. I. Vasil’eva, M. V. Nikiforov, D. Ya. Sidnyaev, N. I. Stepanov, S. P. Tseeva, A. N.
Published in
Computational Mathematics and Mathematical Physics

AbstractA mathematical model of heat transfer between the permafrost foundation of a building with a system of freezing pipes and atmospheric air is constructed and numerically implemented. As a mathematical model of heat transfer in the building foundation, the Stefan problem in the enthalpy statement with smoothed coefficients and a smeared tempe...

Beklaryan, L. A. Beklaryan, A. L.
Published in
Computational Mathematics and Mathematical Physics

AbstractThe existence of a family of bounded soliton solutions for a finite-difference wave equation with a quadratic potential is established. The proof is based on a formalism establishing a one-to-one correspondence between the soliton solutions of an infinite-dimensional dynamical system and the solutions of a family of functional differential ...

Skorokhodov, S. L. Kuzmina, N. P.
Published in
Computational Mathematics and Mathematical Physics

AbstractThe paper presents an analysis of stable and unstable perturbations of ocean currents of a finite transverse scale with a parabolic vertical profiles of velocity (Poiseuille–Couette-type flow), based on the potential vorticity equation in the quasi-geostrophic approximation and taking into account both linear and constant flow velocity shea...

Simakov, S. S.
Published in
Computational Mathematics and Mathematical Physics

AbstractNew boundary conditions in the regions of vessel junctions for a one-dimensional network model of hemodynamics are proposed. It is shown that these conditions ensure the continuity of the solution and its derivatives at the points of vessel junctions. In the asymptotic limit, they give solutions that coincide with the solution in one contin...

Tiryakioglu, B.
Published in
Computational Mathematics and Mathematical Physics

AbstractRadiation of sound waves by a semi-infinite circular cylindrical pipe with non-uniform lining is analyzed by using the Jones’ method in conjunction with the mode matching technique. This mixed method of formulation gives rise to a scalar Wiener–Hopf equation. The inner surface of the duct is coated by acoustically absorbing different lining...

Urev, M. V.
Published in
Computational Mathematics and Mathematical Physics

AbstractThe two-dimensional Stokes problem in a mixed variational statement in a bounded domain with a singular right-hand side given, in particular, by the delta function is considered using an extended scheme for an abstract mixed variational problem. Conditions are established under which a solvability and stability theorem for the solution of a...

Glushko, A. V. Loginova, E. A.
Published in
Computational Mathematics and Mathematical Physics

AbstractAn unsteady heat conduction problem is studied in a plane consisting of two half-planes filled with different inhomogeneous materials with exponential internal thermal conductivities. It is assumed that there is a crack at the boundary of the half-planes, i.e., inhomogeneous transmission conditions are set. In the upper and lower half-plane...