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

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:
vt+sin(x)vx+f(x)ux=0
ut+sin(x)ux+cos(x)vx=0
Thank you
 

hunt_mat

Homework Helper
1,683
12
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

Science Advisor
Homework Helper
41,698
871
You might want to think about the distinction between "boundary conditions" and "initial conditions" and what those differences mean for first order equations.
 

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