Show that the solution is of exponential order

• Sep 24th 2010, 02:14 AM
bkarpuz
Show that the solution is of exponential order
Dear MHF residents,

I wonder to know whether or not there is a way to prove without solving that
the solution of the initial value problem
$
\begin{cases}
\dfrac{\partial}{\partial t}u(t,s)+\dfrac{\partial}{\partial s}u(t,s)=0,\ (t,s)\in D:=\{(t,s):\ t\geq s\geq0\}\\
u(t,0)=u_{0}(t),\ t\in\mathbb{R}_{0}^{+},
\end{cases}
$

where $u_{0}$ is a function of exponential order.