# PDE:Method of characteristics

### From Exampleproblems

solution ,

solution ,

solution Show that if is an integral surface of containing a point , then the surface contains the characteristic curve passing through . (Assume the vector field is ).

solution If and are two graphs that are integral surfaces of and intersect in a curve , show that is a characteristic curve.

solution Solve the initial value problem with and show the solution becomes singular for some unless is a nondecreasing function of .

solution Consider with the IC

Show that a shock develops at a finite time and describe the weak solution.

solution Consider with the IC

Find the weak solution.

solution Consider the problem with condition: on