3-dimensional Wave equation with Cauchy data

Printable View

February 13th 2011, 03:24 PM
leads

3-dimensional Wave equation with Cauchy data

Let $u(x,y,t)$ be the solution of the Cauchy problem
$u_{tt}-c^2 u_{xx}-c^2 u_{yy}=0$ ,
$u(x,y,0)=f(x,y)$ ,
$u_{t}(x,y,0)=g(x,y)$ ,

where $c>0$ is a constant and $f(x,y)$ and $g(x,y)$ vanish for $x^2 +y^2 >r^2$ for some $r>0$ .
Show that the solution $u(x,y,t)$ vanishes if $x^2+y^2-r^2>c^2 t^2$

All times are GMT -8. The time now is 05:00 PM.

Copyright © 2005-2013 Math Help Forum. All rights reserved.

Copyright © 2005-2013 Math Help Forum. All rights reserved.