Inverse Problems for Some Sobolev-Type Mathematical Models
Copyright policy )Inverse Problems for Some Sobolev-Type Mathematical Models
Summary: The present article is devoted to the study of mathematical models based the Sobolev-type equations and systems arising in dynamics of a stratified fluid, elasticity theory, hydrodynamics, electrodynamics, etc. Along with a solution we determine an unknown right-hand side and coefficients in a Sobolev-type equations of the forth order. The overdetermination conditions are the values of a solution in a collection of points of a spatial domain. The problem is reduced to an operator equation whose solvability is established with the help of a priori estimates and the fixed point theorem. The existence and uniqueness theorems of solutions for the linear and nonlinear cases are proven. In the linear case the result is global in time and it is local in the nonlinear case. The main spaces in question are the Sobolev spaces.
- South Ural State University (Южно-Уральский государственный университет) Russian Federation
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the Boussinesq - Love model, математическая модель, волны в плазме, вращающаяся жидкость, the Boussinesq-Love model, THE SOBOLEV-TYPE MODEL,SOBOLEV EQUATION,EXISTENCE AND UNIQUENESS THEOREMS,INVERSE PROBLEM,BOUNDARY VALUE PROBLEM,PLASMA WAVES,ROTATING FLUID,THE BOUSSINESQ LOVE MODEL,МОДЕЛИ СОБОЛЕВСКОГО ТИПА,УРАВНЕНИЕ СОБОЛЕВА,МАТЕМАТИЧЕСКАЯ МОДЕЛЬ,ТЕОРЕМА СУЩЕСТВОВАНИЯ И ЕДИНСТВЕННОСТИ РЕШЕНИЯ,ОБРАТНАЯ ЗАДАЧА,КРАЕВАЯ ЗАДАЧА,ВОЛНЫ В ПЛАЗМЕ,ВРАЩАЮЩАЯСЯ ЖИДКОСТЬ,МОДЕЛЬ БУССИНЕСКА ЛЯВА, обратная задача, уравнение Соболева, теорема существования и единственности решения, plasma waves, the Sobolev-type model, модель Буссинеска - Лява, boundary value problem, inverse problem, rotating fluid, модели Соболевского типа, УДК 517.95, existence and uniqueness theorems, краевая задача, Sobolev equation, Ultraparabolic equations, pseudoparabolic equations, etc.
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