Regularization of Systems of Volterra Linear Integral Equations of the Third Kind

It is studied a regularization of systems of linear Volterra integral equations of the third kind with continuous kernel degenerated at points of the given segment on the diagonal. The determinant of the matrix outside the integral disappears at the starting point or at the end of the segment. Regularizing Lavrent’ev type operator is constructed that preserves the property of Volterra equation. It is proved the uniform convergence of the regularized solution to the exact solution, and defined the conditions of uniqueness of the solution in the Hölder space. Also it is considered the case of systems of third kind Volterra linear integral equations with the approximated right hand side of equation. It is established conditions under which a regularized solution of the equation with approximately given right-hand side can serve as an approximate solution to the original equation.