Fredholm-Volterra integral equation with potential kernel (Q5954789)

The authors consider a Fredholm-Volterra equation of the form NEWLINE\[NEWLINE \iint_\Omega {P(\xi,\eta,t)\over [(x-\xi)^2 + (y-\eta)^2]^{1/2}} d\xi d\eta + \int_0^t F(\tau)P(x,y,\tau) d\tau = f(x,y,t), NEWLINE\]NEWLINE under the condition \(\iint_\Omega P(x,y,t)dx dy = M(t)\), \(t\geq 0\) where \(\Omega \) is a disk with radius \(a\). A method to obtain a finite system of Fredholm integral equations is discussed. Furthermore, certain Fredholm integral equations of the first kind are studied as well.