Problem 1

[Kun Guo]

Build on DW's solution,part c).  For -2t < x < 2t, x+3t> 0, Ï• can be solved the same as in part a). x+2t<0, ψ is the same as x< -2t, which is a constant C, since Ï•+ψ.  The u(x,t)= 1/4exp(-x-2t)+C for -2t < x < 2t. Will this be a correct answer to finish up the question?

[Victor Ivrii]

Build on DW's solution,part c).  For -2t < x < 2t, x+3t> 0, Ï• can be solved the same as in part a). x+2t<0, ψ is the same as x< -2t, which is a constant C, since Ï•+ψ.  The u(x,t)= 1/4exp(-x-2t)+C for -2t < x < 2t. Will this be a correct answer to finish up the question?

Probably, it was obtained already (with lost $C$)