I have my PDEs final this week, and my prof really likes giving us word problems and having us interpret the physical situation into the boundary conditions.
I wanted to confirm the following:
Wave equation
Displacement is given by $u(x,0)$
Velocity is given by $u_t(x,0)$
What are $u_x(x,0)$ and $u_x(x,L)$?
Heat equation
Initial temperature is given by $u(x,0)$
What about $u(x,L)$?
What does $u_x(x,0)$ represent? What about $u_x(x,L)$?
Thanks in advance!