Finite element approximations of the wave equation with Dirichlet boundary data defined on a bounded domain in R2

2006 ◽  
pp. 216-233
Author(s):  
I. Lasiecka ◽  
J. Sokolowski ◽  
P. Neittaanmaki
Keyword(s):  
Finite Element ◽  
Wave Equation ◽  
Bounded Domain ◽  
Boundary Data ◽  
Dirichlet Boundary ◽  
Finite Element Approximations ◽  
Dirichlet Boundary Data

scholarly journals The operatorB*Lfor the wave equation with Dirichlet control

2004 ◽  
Vol 2004 (7) ◽  
pp. 625-634 ◽  
Author(s):  
I. Lasiecka ◽  
R. Triggiani
Keyword(s):  
Wave Equation ◽  
Bounded Domain ◽  
Boundary Control ◽  
Dirichlet Boundary ◽  
Arbitrary Dimension ◽  
Energy Methods ◽  
Smooth Bounded Domain ◽  
Dirichlet Boundary Control

In the case of the wave equation, defined on a sufficiently smooth bounded domain of arbitrary dimension, and subject to Dirichlet boundary control, the operatorB*Lfrom boundary to boundary is bounded in theL2-sense. The proof combines hyperbolic differential energy methods with a microlocal elliptic component.

scholarly journals Solutions toH-systems by topological and iterative methods

2003 ◽  
Vol 2003 (9) ◽  
pp. 539-545 ◽  
Author(s):  
P. Amster ◽  
M. C. Mariani
Keyword(s):  
Iterative Methods ◽  
Boundary Data ◽  
Dirichlet Boundary ◽  
Newton Iteration ◽  
Dirichlet Boundary Data

We studyH-systems with a Dirichlet boundary datag. Under some conditions, we show that if the problem admits a solution for some(H0,g0), then it can be solved for any(H,g)close enough to(H0,g0). Moreover, we construct a solution of the problem applying a Newton iteration.

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