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\begin{document}

\title{CONTROL OF KAWAHARA EQUATION WITH OVERDETERMINATION CONDITION: THE
UNBOUNDED CASES}



\author[1]{Roberto Capistrano Filho}%
\author[1]{S. LUAN Soares de Sousa}%
\author[2]{A. FERNANDO GALLEGO}%
\affil[1]{Universidade Federal de Pernambuco}%
\affil[2]{Universidad Nacional de Colombia Sede Manizales}%


\vspace{-1em}



  
  \date{May 26, 2024}


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\begin{abstract}
Abstract. In this manuscript we consider the internal control problem
for the fifth order KdV type equation, commonly called the Kawahara
equation, on unbounded domains. Precisely, under certain hypotheses over
the initial and boundary data, we are able to prove that there exists an
internal control input such that solutions of the Kawahara equation
satisfies an integral overdetermination condition. This condition is
satisfied when the domain of the Kawahara equation is posed in the real
line, left half-line and right half-line. Moreover, we are also able to
prove that there exists a minimal time in which the integral
overdetermination condition is satisfied. Finally, we show a type of
exact controllability associated with the ``mass'' of the Kawahara
equation posed in the half-line.%
\end{abstract}%



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\textbf{Hosted file}

\verb`Kawahara_Control_Unbounded_Final.tex`  available at \url{https://authorea.com/users/472091/articles/563170-control-of-kawahara-equation-with-overdetermination-condition-the-unbounded-cases}

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