PDE for IVP on R for a transport equation

1. Jul 16, 2013

Robconway

Hi guys, I'm having trouble with a homework problem:

I will have to solve for the IVP of a transport equation on R:

the equations are:

Ut-4Ux=t^2 for t>0, XER
u=cosx for t=0, XER

I've actually never seen a transportation problem like this and any help would be greatly appreciated, thank you!

2. Jul 16, 2013

Staff: Mentor

Have you learned about the method of characteristics? Suppose the right hand side were zero. Would you be able to solve the problem then?

Chet

3. Jul 16, 2013

haruspex

To eliminate the RHS, consider U = V(x, t) +T(t) where V satisfies the homogeneous equation and the same boundary condition.