PDE for IVP on R for a transport equation

[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!

 

[Chestermiller]

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

 

[haruspex]

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