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Math Help - Show that the solution is of exponential order

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    Senior Member bkarpuz's Avatar
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    Exclamation 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
    <br />
\begin{cases}<br />
\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\}\\<br />
u(t,0)=u_{0}(t),\ t\in\mathbb{R}_{0}^{+},<br />
\end{cases}<br />
    where u_{0} is a function of exponential order.
    Last edited by bkarpuz; September 24th 2010 at 06:55 AM.
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