Regularity and Strong Convergence of a Variational Approximation to a Nonhomogeneous Dirichlet Hyperbolic Boundary Value Problem

1988 ◽  
Vol 19 (3) ◽  
pp. 528-540 ◽  
Author(s):  
Irena Lasiecka ◽  
Jan Sokolowski
Keyword(s):  
Boundary Value Problem ◽  
Strong Convergence ◽  
Boundary Value ◽  
Variational Approximation ◽  
Hyperbolic Boundary

Hyperbolic Boundary-Value Problem for a Piecewise Homogeneous Hollow Cylinder

2020 ◽  
Vol 71 (12) ◽  
pp. 1843-1854
Author(s):  
A. P. Gromyk ◽  
I. M. Konet ◽  
T. M. Pylypiuk
Keyword(s):  
Boundary Value Problem ◽  
Hollow Cylinder ◽  
Boundary Value ◽  
Hyperbolic Boundary

scholarly journals Constraints Optimal Control Governing by Triple Nonlinear Hyperbolic Boundary Value Problem

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Jamil A. Ali Al-Hawasy ◽  
Lamyaa H. Ali
Keyword(s):  
Optimal Control ◽  
Boundary Value Problem ◽  
Existence Theorem ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Continuous Control ◽  
Control Vector ◽  
State Equations ◽  
Vector Solution ◽  
Hyperbolic Boundary

The focus of this work lies on proving the existence theorem of a unique state vector solution (Stvs) of the triple nonlinear hyperbolic boundary value problem (TNHBVP) when the classical continuous control vector (CCCVE) is fixed by using the Galerkin method (Galm), proving the existence theorem of a unique constraints classical continuous optimal control vector (CCCOCVE) with vector state constraints (equality EQVC and inequality INEQVC). Also, it consists of studying for the existence and uniqueness adjoint vector solution (Advs) of the triple adjoint vector equations (TAEqs) associated with the considered triple state equations (Tsteqs). The Fréchet Derivative (Frde.) of the Hamiltonian (HAM) is found. At the end, the theorems for the necessary conditions and the sufficient conditions of optimality (Necoop and Sucoop) are achieved.

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