How many B.C. are necessary for first order PDE set?

[dragonmount]

Hi
I have a set of two linearized integro-partial-differential equations with derivatives of first order (also inside the integrals). How many boundary (initial) conditions should I give for such problem for the solution to be unique? is the 'initial condition that intersect once with the characteristics' still holds? If you can add a refernce that I can use in front of my supervisior it will be great.
A simple problem that reflects my difficulties:
v_t+sin(x)v_x+f(x)u_x=0
u_t+sin(x)u_x+cos(x)v_x=0
Thank you

 

[hunt_mat]

We're not here to do your research for you, but I will explain one thing to you. You can calculate Riemann invariants for the system you gave and these are constant on the characteristics and so you will only require 2 initial conditions .

 

[HallsofIvy]

You might want to think about the distinction between "boundary conditions" and "initial conditions" and what those differences mean for first order equations.