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In this text matrix Volterra integral equation of the first kind isaddressed. It is assumed that kernels of the equation have jump discontinuitieson non-intersecting curves. Such equations appear in the theory of evolvingdynamic systems. Differentiation of such equations with jump discontinuekernels yields the new class of the Volterra integral equations withfunctionally perturbed argument. The algorithm for construction of thelogarithmic power asymptotics of the desired continuous solutions is proposed.The theorem of existance of the parametric families of solutions is proved.Finally the sufficient conditions for existence and uniqueness of continuoussolution are derived.

Solution to the Volterra Matrix Equation of the 1st kind with Piecewise Continuous Kernels