Abstract
Regular and singular asymptotic methods are applied to one- and two-dimensional Fredholm–Volterra integral equation (F–VIE) of the first kind that arise in the treatment of various two-dimensional axisymmetric and three-dimensional problems with mixed boundary conditions in the mechanics of continuous media. The solution of the integral equation is obtained in the space
L
2(Ω)×C(0,T),
0⩽t⩽T<∞
under certain conditions, where
Ω is the domain of integration and
t∈(0,
T) is the time interval.