Reconstruction of a Source Term in a Hyperbolic Equation
Daurenbek Serikbaev
Institute of Mathematics and Mathematical Modeling, Almaty Kazakhstan
Co-Author(s):
Abstract:
We consider the wave equation
\begin{equation}
u_{tt}-a(x)u_{xx}=f,\;\;\;(t,x)\in(0,T)\times(0,l),
\end{equation}
with suitable initial and boundary conditions. Using an additional boundary measurement at $x=l$,
we study the identification of an unknown source term $f$. The analysis is
based on Carleman estimates for the wave operator; see \cite{BY17}.
\textbf{Funding}: This research is funded by the Science Committee of the Ministry of Science and Higher Education of the
Republic of Kazakhstan (Grant No. AP23485971).
\begin{thebibliography}{6}
\bibitem{BY17} M. Bellassoued, M. Yamamoto. Carleman Estimates and Applications to Inverse Problems
for Hyperbolic Systems, Springer, Cham, 2017.
\end{thebibliography}