Abstract
In this paper, the solution, in a series form, of the integral equation of the mixed type in the space
L(Ω)×C[0,T] is obtained, where
Ω={(x,y,z):−∞<x,y<∞,−∞<z<0} and the time
t∈[0,T],
0⩽t⩽T<∞
. The existence and the uniqueness of the solution of the integral equation is considered. The solution of the integral equation in a series form is obtained and the convergence is discussed.