\documentclass[12pt]{article}
\begin{document}
\begin{center}
{\it Min-max gam problem and Riccati equation} 

\vspace{.10in}


{\bf Jing Zhang}\\
University of Virginia\\
{\tt jz4f@virginia.edu} 
\end{center}

\vspace{.10in} 

\noindent {\bf Abstract}:  Min-max control problems defined for a large class
of PDE models will be considered. A distinct feature of the problems under
consideration is the fact that control function (counteracting potential
disturbances in minimizing given objective) acting upon the system
distributionally (not functionally). This happens typically when a control has
very small support such as bounded or point controls. Our goal is to establish
well-posedness of a non-standard Riccati equation, where the solution yields a
feedback operator deriving the optimal solution. Our work deals with
non-smoothing dynamics as they arise in hyperbolic-like problems. We shall
show that under the assumption of  singular estimate imposed on the dynamics
(A, B), (A the generator, B the control), well-posedness of Riccati equation
is guaranteed and the solution for min-max problem can be derivated by solving
Riccati equation. 
              
The assumption is motivated by a new class of controlled systems that is
arising in hyperbolic-parabolic interacting (coupled system) such as: 

\begin{itemize} 
\item structured acoustic model; 
\item fluid structure model; 
\item thermoelastic plate model; 
\end{itemize}

The detailed formulation of the problem is given later. 

\end{document} 