Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 1031.35148
Feng, Xiaobing; Lenhart, Suzanne; Protopopescu, Vladimir; Rachele, Lizabeth; Sutton, Brian
Identification problem for the wave equation with Neumann data input and Dirichlet data observations. (English)
[J] Nonlinear Anal., Theory Methods Appl. 52, No.7, A, 1777-1795 (2003). ISSN 0362-546X

The identification of the dispersive coefficient $h(x)\in L^\infty$ in the wave equation in a bounded domain $\Omega$ with $C^2$ boundary $$\gather u_{tt}-\Delta u= h(x)u+ f(x,t),\quad (x,t)\in \Omega\times (0,T),\quad f\in L^2,\\ u(x,0)= u_0\in H^1(\Omega),\quad u_t(x,0)= u_1\in L^2(\Omega),\quad x\in\Omega,\\ {\partial u\over\partial n}= g\in H^{1/2}(\partial\Omega\times (0,T))\endgather$$ is obtained by minimizing the Tikhonov functional $$J_\beta(h):= {1\over 2} \Biggl(\int_{\partial\Omega\times (t_1,t_2)} (u(h)- z)^2 ds dt+ \beta \int_\Omega h^2 dx\Biggr),$$ over $h\in L^\infty(\Omega)$, where $z\in L^2(\partial\Omega\times (t_1,t_2))$ with $0\le t_1< t_2\le T$, is a given data for $u|_{\partial\Omega\times (t_1,t_2)}$. However, no criterion for choosing the regularization parameter $\beta> 0$ is given. Furthermore, some of the numerically obtained results for $h(x)$ are 50\% out of the corresponding analytical solution, showing that a more accurate numerical method for solving the nonlinear control problem is needed in any future work.
[D.Lesnic (Leeds)]

MSC 2000:: *35R30 Inverse problems for PDE
35L05 Wave equation
65M32 Inverse problems

Keywords: coefficient identification; wave equation; optimal control; Dirichlet-Neumann map; Tikhonov's regularization

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]