35Fxx General first-order equations and systems

35F05  General theory of linear first-order PDE
35F10  Initial value problems for linear first-order PDE, linear
               evolution equations
35F15  Boundary value problems for linear first-order PDE
35F20  General theory of nonlinear first-order PDE
35F25  Initial value problems for nonlinear first-order PDE,
               nonlinear evolution equations
35F30  Boundary value problems for nonlinear first-order PDE
35F99  None of the above but in this section