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Thread: Show that the solution is of exponential order

  1. September 24th 2010, 02:14 AM #1
    bkarpuz
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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 05:55 AM.
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