Solution to a linear system of PDE's

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I faced the following problem of linear system of PDE's

1: dX/ds+dX/di+(g*Y(i)+w)*X(s,i)=0
2: dY/ds+dY/di-(g*Y(i)-v-w)*Y(s,i)=0,

where Y(i)=int_0^infty Y(s,i)ds and g, w, and v are scalars. The 
conditions are
X(s,0)=w
Y(s,0)=0
S(0,i)=1/i

Does anyone have an idea how to proceed or to solve this? Even some 
references?

Thanks,

Erick