Published in Journal of Applied and Industrial Mathematics
Abstract We construct a numerical method for recovering a variable coefficient in the Cauchy problem and also in the initial boundary value problem for the one-dimensional heat equation. The desired coefficient is assumed to be time-dependent but not space-dependent. Our approach is based on the construction of an auxiliary ordinary differential eq...
Published in Journal of Applied and Industrial Mathematics
Abstract In connection with the topical problem of creating comfortable atmosphere in urban environment, we present a mathematical algorithm for allocating quotas of harmful emissions between its sources in a megacity. Our construction is based on some recently developed method of optimal distribution of limited resources between differentiated gro...
Published in Journal of Applied and Industrial Mathematics
Abstract In this paper, we introduce a nonlinear Lanchester-type model involving supply units. The model describes a battle where the Blue party consisting of one armed force \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgree...
Published in Journal of Applied and Industrial Mathematics
Abstract Some direct numerical method is presented for solving the inverse coefficient problem for an elliptic equation with piecewise constant coefficients. The discontinuity points of the coefficients are assumed known. The algorithm is based on the theory of spectral problems of linear algebra and the application of finite-difference methods for...
Published in Journal of Applied and Industrial Mathematics
Abstract The Radon transform is a major integral transform in computed tomography and a widely applied technique in computer vision and image analysis which is used to detect linear structures and regular textures. Its application is based on the property of the integrals of the direct problem to accumulate the image brightness along the contours u...
Published in Journal of Applied and Industrial Mathematics
Abstract We pose the direct and inverse problems of finding the electromagnetic field and the diagonal memory matrix for the reduced canonical system of integro-differential Maxwell’s equations. The problems are replaced by a closed system of Volterra-type integral equations of the second kind with respect to the Fourier transform in the space vari...
Published in Journal of Applied and Industrial Mathematics
Abstract We study the system of two fourth-order nonlinear hyperbolic partial differential equations. The right-hand sides of the equations contain double Laplace operators and the squares of the gradients of the sought functions. Such equations, close to the Boussinesq equation and the Navier–Stokes equations, occur in problems of hydrodynamics. W...
Published in Journal of Applied and Industrial Mathematics
Abstract We study the problem of optimal location of the ambulance fleet at the base stations. The objective is to minimize the average waiting time for ambulance arrival. We elaborate a simulation model that describes a workday of the emergency medical service (EMS). This model takes into account the stochastic nature of the problem and the change...
Published in Journal of Applied and Industrial Mathematics
Abstract We consider the problem of the flow of a viscous fluid in the presence of solid bodies (namely, the two walls and a permeable plate) under time-periodic forcing. The formulation of the problem includes the Navier–Stokes equations, the equation of continuity, and the boundary conditions at the solid boundaries. The new hydromechanical effec...
Published in Journal of Applied and Industrial Mathematics
Abstract We study the system of equations which bases on the one-dimensional Schrödinger equation and connects the potential, amplitude, and phase functions. Using the methods of compatibility theory of systems of partial differential equations, we obtain the completely integrable systems that connect only two functions of the above three. As a cor...
