**Tariel Kiguradze**

## Some Boundary Value Problems for Systems of Linear Partial Differential Equations of Hyperbolic Type

**abstract:**

The linear hyperbolic system
\begin{equation}
\frac{\pa^2 u}{\pa x\pa y}=\cp_0(x,y)u+\cp_1(x,y)\frac{\pa u}{\pa x}+
\cp_2(x,y)\frac{\pa u}{\pa y}+q(x,y)\tag{$1$}
\end{equation}
is considered, where $\cp_0,\;\cp_1,\;\cp_2$ and $q$ are respectively
the $\nn$ matrices and the $n$-dimensional vector whose components are
measurable and essentially bounded functions in the rectangle
$\cd_{ab}=[0,a]\tm[0,b]$ or in the strip $\cd_b=\linebreak =\br\tm[0,b]$.
For system (1) problems with general functional boundary conditions
are investigated in the rectangle $\cd_{ab}$ and problems on bounded,
almost-periodic and periodic solutions in the strip $\cd_b$.
Optimal in a certain sense conditions are established, guaranteeing the unique
solvability of the problems and the stability of their solutions with
respect to small perturbations of the coefficients of system (1) and of
the boundary conditions.

**Mathematics Subject Classification:**
35L55

**Key words and phrases:**
System of partial differential equations
of hyperbolic type, boundary value problem in the rectangle, classical
solution, absolutely continuous solution, generalized solution,
periodic solution, almost-periodic solution,
bounded solution.