Regularization of a Volterra integral equation by linear inequalities (Q911737)

The authors consider a triple of positive functions \((p,v,x)\in C(0,1)\times C(0,1)\times C^ 1(0,1)\) and a pair of auxiliary functions (Q,b)\(\in C(0,1)\times C(0,1)\) satisfying the convolution integral equation \(\int^{t}_{0}x(t-s)dQ(s)=b(t),\) where \(Q(t)=(v(t)/p(t)),\quad b(t)=p(t)-p(0)\quad (0\leq t\leq 1).\) The determination of a monotone nonincreasing and convex response function x arising in reservoir mechanics is investigated from the computational point of view. Three versions of regularization by linear inequalities are formulated and discussed.