A Dirichlet Boundary Control Problem for the Strongly Damped Wave Equation

1992 ◽  
Vol 30 (5) ◽  
pp. 1092-1100 ◽  
Author(s):  
Francesca Bucci
Keyword(s):  
Wave Equation ◽  
Control Problem ◽  
Boundary Control ◽  
Dirichlet Boundary ◽  
Damped Wave Equation ◽  
Dirichlet Boundary Control ◽  
Boundary Control Problem ◽  
Strongly Damped Wave Equation ◽  
Strongly Damped

scholarly journals Crank-Nicolson finite difference schemes for parabolic optimal Dirichlet boundary control problem

2021 ◽  
Author(s):  
Caijie Yang ◽  
Tongjun Sun
Keyword(s):  
Finite Difference ◽  
Control Problem ◽  
Boundary Control ◽  
Dirichlet Boundary ◽  
Second Order ◽  
Difference Schemes ◽  
Optimality System ◽  
Finite Difference Schemes ◽  
Dirichlet Boundary Control ◽  
Boundary Control Problem

In this paper, we adopt the optimize-then-discretize approach to solve parabolic optimal Dirichlet boundary control problem. First, we derive the first-order necessary optimality system, which includes the state, co-state equations and the optimality condition. Then, we propose Crank-Nicolson finite difference schemes to discretize the optimality system in 1D and 2D cases, respectively. In order to build the second order spatial approximation, we use the ghost points on the boundary in the schemes. We prove that the proposed schemes are unconditionally stable, compatible and second-order convergent in both time and space. To avoid solving the large coupled schemes directly, we use the iterative method. Finally, we present a numerical example to validate our theoretical analysis.

Approximate controllability of semilinear impulsive strongly damped wave equation

2015 ◽  
Vol 21 (1) ◽  
Author(s):  
Hanzel Larez ◽  
Hugo Leiva ◽  
Jorge Rebaza ◽  
Addison Ríos
Keyword(s):  
Fixed Point ◽  
Wave Equation ◽  
Fixed Point Theorem ◽  
Boundary Conditions ◽  
Approximate Controllability ◽  
Dirichlet Boundary ◽  
Dirichlet Boundary Conditions ◽  
Damped Wave Equation ◽  
Strongly Damped Wave Equation ◽  
Strongly Damped

AbstractRothe's fixed-point theorem is applied to prove the interior approximate controllability of a semilinear impulsive strongly damped wave equation with Dirichlet boundary conditions in the space

scholarly journals Error bounds for a Dirichlet boundary control problem based on energy spaces

2016 ◽  
Vol 86 (305) ◽  
pp. 1103-1126 ◽  
Author(s):  
Sudipto Chowdhury ◽  
Thirupathi Gudi ◽  
A. K. Nandakumaran
Keyword(s):  
Control Problem ◽  
Boundary Control ◽  
Error Bounds ◽  
Dirichlet Boundary ◽  
Dirichlet Boundary Control ◽  
Boundary Control Problem
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