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S. A. Gabov

Bio: S. A. Gabov is an academic researcher. The author has contributed to research in topics: Nonlinear system. The author has an hindex of 1, co-authored 1 publications receiving 9 citations.

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TL;DR: In this article, the authors present new mathematical results in the theory of linear and nonlinear waves on the surface of a flotation liquid, and prove the existence of nonlinear standing waves within the framework of an exact physical model.
Abstract: This survey presents new mathematical results in the theory of linear and nonlinear waves on the surface of a flotation liquid. A flotation liquid is a liquid on whose surface heavy particles are floating; the particles may consist of arbitrary materials or may be particles of frozen liquid. The first part of the article considers initial- and boundary-value problems in the theory, their solvability, and the behavior of the solutions over long periods. In the second part of the survey, theorems are proved on the existence of nonlinear standing waves within the framework of an exact physical model, and both internal and free waves are considered. Also, the fundamental equations for shallow flotation waves are derived and examined.

9 citations


Cited by
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TL;DR: To the best of our knowledge, there is only one application of mathematical modelling to face recognition as mentioned in this paper, and it is a face recognition problem that scarcely clamoured for attention before the computer age but, having surfaced, has attracted the attention of some fine minds.
Abstract: to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

3,015 citations

Journal ArticleDOI
TL;DR: In this paper, the authors study the problem on small motions of ideal stratified fluid with a free surface, partially covered by crumbling ice, and find sufficient existence conditions for existence of a strong (with respect to the time variable) solution to the initial-boundary value problem describing evolution of the specified hydrodynamics system.
Abstract: We study the problem on small motions of ideal stratified fluid with a free surface, partially covered by crumbling ice. By the method of orthogonal projecting the boundary conditions on the moving surface and, with the help of investigation of some auxiliary problems, the original initial-boundary value problem is reduced to the equivalent Cauchy problem for a second order differential equation in a Hilbert space. We find sufficient existence conditions for existence of a strong (with respect to the time variable) solution to the initial-boundary value problem describing evolution of the specified hydrodynamics system.

3 citations

01 Jan 2018
TL;DR: In this article, the authors studied the problem of small motions of two non-mixing ideal stratified fluids with a free surface, covered with crumbling ice, and found sufficient existence conditions for a strong (with respect to the time variable) solution of the initial-boundary value problem describing the evolution of the specified hydrodynamics system.
Abstract: We study the problem on small motions of two non mixing ideal stratified fluids with a free surface, covered with crumbling ice. Using method of orthogonal projecting the boundary conditions on the moving surface and the introduction of auxiliary problems of the original initial-boundary value problem is reduced to the equivalent Cauchy problem for a differential equation of second order in some Hilbert space. We find sufficient existence conditions for a strong (with respect to the time variable) solution of the initial-boundary value problem describing the evolution of the specified hydrodynamics system.

2 citations

Journal ArticleDOI
TL;DR: In this paper, the authors studied the problem of small motions of an ideal stratified liquid whose free surface consists of three regions: liquid surface without ice, a region of elastic ice, and an area of crumbled ice.
Abstract: We study the problem of small motions of an ideal stratified liquid whose free surface consists of three regions: liquid surface without ice, a region of elastic ice, and a region of crumbled ice. The elastic ice is modeled by an elastic plate. The crumbled ice is understood as weighty particles of some matter floating on the free surface. Using the method of orthogonal projection of boundary conditions on a moving surface and the introduction of auxiliary problems, we reduce the original initial boundary value problem to an equivalent Cauchy problem for a second-order differential equation in a Hilbert space. We obtain conditions under which there exists a strong (with respect to time) solution of the initial boundary value problem describing the evolution of the hydrodynamic system under consideration.

1 citations

Journal ArticleDOI
TL;DR: In this article, the authors considered a mechanical system consisting of water covered by brash ice and a body freely floating near equilibrium, where the water occupies a half-space into which an infinitely long surface-piercing cylinder is immersed, thus allowing us to study two-dimensional modes of the coupled motion, which is assumed to be of small amplitude.
Abstract: A mechanical system consisting of water covered by brash ice and a body freely floating near equilibrium is considered. The water occupies a half-space into which an infinitely long surface-piercing cylinder is immersed, thus allowing us to study two-dimensional modes of the coupled motion, which is assumed to be of small amplitude. The corresponding linear setting for time-harmonic oscillations reduces to a spectral problem whose parameter is the frequency. A constant that characterises the brash ice divides the set of frequencies into two subsets and the results obtained for each of these subsets are essentially different. For frequencies belonging to a finite interval adjacent to zero, the total energy of motion is finite and the equipartition of energy holds for the whole system. For every frequency from this interval, a family of motionless bodies trapping waves is constructed by virtue of the semi-inverse procedure. For sufficiently large frequencies outside of this interval, all solutions of finite energy are trivial.

1 citations