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arXiv · 1204.5549

Solution to the Volterra integral equations of the first kind with piecewise continuous kernels in class of Sobolev-Schwartz distributions

Denis Sidorov
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Abstract

Sufficient conditions for existence and uniqueness of the solution of the Volterra integral equations of the first kind with piecewise continuous kernels are derived in framework of Sobolev-Schwartz distribution theory. The asymptotic approximation of the parametric family of generalized solutions is constructed. The method for the solution's regular part refinement is proposed using the successive approximations method.

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Denis Sidorov. 2012-04-25. Solution to the Volterra integral equations of the first kind with piecewise continuous kernels in class of Sobolev-Schwartz distributions. https://arxiv.org/abs/1204.5549

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