Examines solvability and uniqueness of solutions in degenerate Volterra integro-differential equations, highlighting their importance in mathematical modeling.
Systems of linear Volterra integro-differential equations with convolution type kernels and constant coefficient matrices are considered. It is assumed that the matrix multiplying the higher derivatives of the unknown vector function is singular. A new statement of the initial-value problem different from the conventional statement of a Cauchy problem is considered. Conditions for the solvability of such systems and for the existence and uniqueness of solutions to initial-value problems are obtained. Theoretical results are illustrated by examples.
No takes yet. Share an insight, caveat, or question.
Chistyakov et al. (2026) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: