Is exist the not smooth distribution which satisfying:
$\left ( D_{t}^{2}-D_{x}^{2} \right )u(x,t)=0$
I can't find at least one not smooth distribution like this...
Thanks for the help!
Is exist the not smooth distribution which satisfying:
$\left ( D_{t}^{2}-D_{x}^{2} \right )u(x,t)=0$
I can't find at least one not smooth distribution like this...
Thanks for the help!
A classic! This example upset a lot of people c. 1800 and even before. It it the one-dimensional wave equation. For any distribution $v$, $u_{\pm} (x,t)=v(x\pm t)$ (suitably interpreted) solves that equation. "Suitably interpreted" is just a generalization of what it should mean for classical functions, but can be made precise in several (provably equivalent) ways: let $T_x$ be translation of functions or distributions, then "$v(x+t)$" can be defined as $T_x v$, where the dummy variable is $t$.