Discuss a method of the characteristics

Question

Solve the below:

1. Use method of the characteristics to solve the following (PDE)

u_t+3uu_x=0
for initial condition

u(x,0)={5 x<0
            1 x>0}

2. Solve the above equation

u_t+3uu_x=0
for initial condition

u(x,0)={1 x<2

           3 x>2}

3. Solve

∂²u/∂t² = c²∂²u/∂x²

subject to the conditions:

u(x,0)=0, ∂u/∂x(x,0)=0 and ∂u/∂x(0,t)=g(t)