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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

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

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