On the Uniqueness Theorem for Generalized Solutions of Initial-Boundary Problems for the Marguerre—Vlasov Vibrations of Shallow Shells with Clamped Boundary Conditions

1999 ◽  
Vol 39 (3) ◽  
pp. 309-326 ◽  
Author(s):  
V. I. Sedenko
Keyword(s):  
Boundary Conditions ◽  
Uniqueness Theorem ◽  
Initial Boundary ◽  
Generalized Solutions ◽  
Boundary Problems ◽  
Shallow Shells ◽  
The Uniqueness Theorem

THE METHOD OF REAL BOUNDARY PROBLEMS DEVELOPING THE REAL BOUNDARY CONDITIONS

2016 ◽  
Vol 9 (1) ◽  
pp. 11-13
Author(s):  
Котов ◽  
P. Kotov
Keyword(s):  
Heat Transfer ◽  
Boundary Conditions ◽  
Efficient Solution ◽  
Initial Boundary ◽  
Heat Propagation ◽  
Initial Boundary Value Problems ◽  
Boundary Problems ◽  
The Real ◽  
Real Equation ◽  
Initial Boundary Value

An efficient solution to the real equation of heat transfer with deterministic disturbance and informative method of the basic initial-boundary value problems for the unsteady heat propagation with measurable initial and boundary conditions.

scholarly journals Generalized solutions to singular initial-boundary hyperbolic problems with non-Lipshitz nonlinearities

2006 ◽  
Vol 133 (31) ◽  
pp. 87-99 ◽  
Author(s):  
Irina Kmit
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Nonlinear Boundary ◽  
Hyperbolic Systems ◽  
Initial Boundary ◽  
Nonlinear Boundary Conditions ◽  
Generalized Solutions ◽  
Hyperbolic Problems ◽  
Colombeau Algebra ◽  
Semilinear Hyperbolic Systems

We prove the existence and uniqueness of global generalized solutions in a Colombeau algebra of generalized functions to semilinear hyperbolic systems with nonlinear boundary conditions. Our analysis covers the case of non-Lipschitz nonlinearities both in the differential equations and in the boundary conditions. We admit strong singularities in the differential equations as well as in the initial and boundary conditions. AMS Mathematics Subject Classification (2000): 35L50, 35L67, 35D05.

Electromagnetic Fields Theory of Electrical Machines Part II: Uniqueness Theorem for Time-Varying Electromagnetic Fields in Hysteretic Media

2005 ◽  
Vol 42 (2) ◽  
pp. 203-208 ◽  
Author(s):  
Saurabh Kr. Mukerji ◽  
Sandeep Kr. Goel ◽  
Sunil Bhooshan ◽  
Kartik Prasad Basu
Keyword(s):  
Boundary Conditions ◽  
Uniqueness Theorem ◽  
Unique Solution ◽  
Electromagnetic Fields ◽  
Bachelor's Degree ◽  
Electrical Machines ◽  
Time Varying ◽  
Initial Condition ◽  
Free Media ◽  
The Uniqueness Theorem

Conditions resulting in a unique solution of Maxwell's equations are investigated. For this purpose, time-varying electromagnetic fields in media exhibiting a linearized form of hysteresis are considered. The treatment is an extension of the uniqueness theorem for electromagnetic fields in hysteresis-free media. The major conclusions are that there is no initial condition for fields in lossy regions, however, boundary conditions must be satisfied for all values of time. The treatment presented may be useful to students preparing for a masters degree or final year bachelor's degree.

scholarly journals REFINED MODEL OF VISCO-ELASTIC-PLASTIC DEFORMATION OF REINFORCED FLEXIBLE SHALLOW SHELLS

2019 ◽  
Vol 81 (4) ◽  
pp. 461-473
Author(s):  
A.P. Yankovskii
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Plastic Behavior ◽  
Face Surface ◽  
Shallow Shells ◽  
Elastic Plastic ◽  
Initial Boundary Value

The initial-boundary value problem of the visco-elastic-plastic behavior of flexible shallow shells reinforced along parallel surfaces is formulated. The inelastic behavior of the materials of the components of the composition is described by the equations of the theory of plastic flow with isotropic hardening. Viscoelastic deformation is determined by the relations of the Maxwell -Boltzmann model. Geometric nonlinearity is taken into account in the Karman approximation. The obtained resolving equations and boundary conditions allow with varying degrees of accuracy to determine the stress-strain state (including the residual state) in the components of the composition of curved panels. The low resistance of the reinforced structure to transverse shear is taken into account. In the first approximation, the equations and boundary conditions corresponding to the traditional non-classical Reddy theory follow from the relations obtained. The numerical solution of the formulated initial-boundary value problem is based on an explicit “cross” scheme. The features of visco-elastic-plastic dynamic deformation of an orthogonal reinforced cylindrical rectangular panel under the action of a load caused by an air blast wave are investigated. It is shown that in some cases even for relatively thin reinforced shallow shells, Reddy's theory is unacceptable for obtaining adequate results of calculations of their visco-elastic-plastic dynamic behavior. It has been demonstrated that the shape and size of the residual deflections of curved composite panels substantially depend on which face surface of the structure (convex or concave) an external load is applied. It was found that in both cases of loading, residual deflections lead to the formation of longitudinal folds in a thin cylindrical reinforced panel.

scholarly journals Thermoelasticity without energy dissipation for initially stressed bodies

2002 ◽  
Vol 31 (6) ◽  
pp. 329-337 ◽  
Author(s):  
Jun Wang ◽  
Susan Palmer Slattery
Keyword(s):  
Energy Dissipation ◽  
Uniqueness Theorem ◽  
Large Deformation ◽  
Linear Theory ◽  
Initial Boundary ◽  
Initial Boundary Value Problems ◽  
Nonuniform Temperature ◽  
Initial Boundary Value ◽  
Without Energy Dissipation ◽  
The Uniqueness Theorem

Thermoelastic equations without energy dissipation are formulated for a body which has previously received a large deformation and is at nonuniform temperature. A linear theory of thermoelasticity without energy dissipation for prestressed bodies is derived and the uniqueness theorem for a class of mixed initial-boundary value problems is established.

scholarly journals The Time-fractional Airy Equation on the Metric Graph

2021 ◽  
pp. 376-388
Author(s):  
Kamoladdin Rakhimov ◽  
Zarifboy Sobirov
Keyword(s):  
Boundary Value Problem ◽  
Uniqueness Theorem ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Paper Properties ◽  
Metric Graph ◽  
Airy Equation ◽  
Initial Boundary Value ◽  
The Uniqueness Theorem

Initial boundary value problem for the time-fractional Airy equation on a graph with finite bonds is considered in the paper. Properties of potentials for this equation are studied. Using these properties the solutions of the considered problem were found. The uniqueness theorem is proved using the analogue of Gr¨onwall-Bellman inequality and a-priory estimate

scholarly journals REFINED MODEL OF VISCO-ELASTIC-PLASTIC DEFORMATION OF REINFORCED FLEXIBLE SHALLOW SHELLS

2019 ◽  
Vol 81 (4) ◽  
pp. 462-474
Author(s):  
A.P. Yankovskii
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Plastic Behavior ◽  
Face Surface ◽  
Shallow Shells ◽  
Elastic Plastic ◽  
Initial Boundary Value

The initial-boundary value problem of the visco-elastic-plastic behavior of flexible shallow shells reinforced along parallel surfaces is formulated. The inelastic behavior of the materials of the components of the composition is described by the equations of the theory of plastic flow with isotropic hardening. Viscoelastic deformation is determined by the relations of the Maxwell -Boltzmann model. Geometric nonlinearity is taken into account in the Karman approximation. The obtained resolving equations and boundary conditions allow with varying degrees of accuracy to determine the stress-strain state (including the residual state) in the components of the composition of curved panels. The low resistance of the reinforced structure to transverse shear is taken into account. In the first approximation, the equations and boundary conditions corresponding to the traditional non-classical Reddy theory follow from the relations obtained. The numerical solution of the formulated initial-boundary value problem is based on an explicit “cross” scheme. The features of visco-elastic-plastic dynamic deformation of an orthogonal reinforced cylindrical rectangular panel under the action of a load caused by an air blast wave are investigated. It is shown that in some cases even for relatively thin reinforced shallow shells, Reddy's theory is unacceptable for obtaining adequate results of calculations of their visco-elastic-plastic dynamic behavior. It has been demonstrated that the shape and size of the residual deflections of curved composite panels substantially depend on which face surface of the structure (convex or concave) an external load is applied. It was found that in both cases of loading, residual deflections lead to the formation of longitudinal folds in a thin cylindrical reinforced panel.

ON THE SOLVABILITY OF A MIXED PROBLEM WITH DEGREE LAPLACE OPERATORS WITH NONLOCAL BOUNDARY CONDITIONS

2020 ◽  
pp. 85-104
Author(s):  
Shakirbai G. Kasimov ◽  
◽  
Mahkambek M. Babaev ◽  
◽  
Keyword(s):  
Boundary Conditions ◽  
Spectral Problem ◽  
Nonlocal Boundary ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Nonlocal Boundary Conditions ◽  
Laplace Operators ◽  
Initial Boundary Problem ◽  
Initial Boundary Value ◽  
Delayed Time

The paper studies a problem with initial functions and boundary conditions for partial differential partial equations of fractional order in partial derivatives with a delayed time argument, with degree Laplace operators with spatial variables and nonlocal boundary conditions in Sobolev classes. The solution of the initial boundary-value problem is constructed as the series’ sum in the eigenfunction system of the multidimensional spectral problem. The eigenvalues are found for the spectral problem and the corresponding system of eigenfunctions is constructed. It is shown that the system of eigenfunctions is complete and forms a Riesz basis in the Sobolev subspace. Based on the completeness of the eigenfunctions system the uniqueness theorem for solving the problem is proved. In the Sobolev subspaces the existence of a regular solution to the stated initial-boundary problem is proved.

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