Regarding choosing correct boundary condition

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Hi,
I have a condition where at the left boundary and the right boundary I need the flux to be non-zero.
Thus, the equations
pL + qL*fL = 0 and pr + qr*fr = 0 are such that fL and fr being non zero is making my equation hard to determine the values for pl, ql as well as pr, qr.
Plz tell me how should I approach for the same.
with regards,
rc