We study a three-dimensional model Volterra-type integralequation with boundary weakly singular, singular, and strongly singularkernels in the domain $ \Omega=\{(x,y,z):0\leq a<x<\infty $ , $ 0\leq b<y<b_{0} $ , $ 0\leq c<z<c_{0}\} $ which can be called a rectangular pipe.In the case that the coefficients of the equation areconnected with each other, a solution to the equation is sought in the classof continuous functions in $ \Omega $ vanishing with a specifiedasymptotic behavior on special domains.We prove under some conditions that the problem offinding a solution to a three-dimensional integral Volterra-type equation withboundary weakly singular, singular, and strongly singular kernelsreduces to solving one-dimensional integral Volterra-type equations with special boundary kernels.Solving the given integral equations, we employ connections of the latter equations withfirst-order differential equations with weakly singular, singularand strongly singular coefficients. Also, we establishthat there is no need to require the differentiability of a solution and a right-hand side.It suffices that the right-hand side ofthe three-dimensional integral equation with boundary singularweakly singular, and strongly singular kernels is continuous andvanishes with a specified asymptotics on special domains. We provethat, depending on the sign of the coefficients of the equation,the explicit solution to a three-dimensional model Volterra-typeintegral equation with singular kernels can contain from one to threearbitrary functions of two variables. We also describe the casethat there is a unique solution to the integral equation.
