A matrix Volterra integrodifferential equation occurring in polymer rheology (Q803467)

The deformation of a small cube-shaped sample elastic liquid can be approximately described by a symmetric \(3\times 3\) matrix, if material effects are ignored. These matrices obey an ordinary first order Volterra integrodifferential equation. The author discusses a singularly perturbed Volterra integrodifferential equation on a manifold, presents an existence and uniqueness theorem, asymptotic results and a study of the solutions. Since many equations in this paper can be solved directly using Lemma 1 and its corollaries [cf. the reviewer, Acta. Math. Appl. Sin. 5, 274-284 (1982; Zbl 0492.34002)], some new results can be deduced. The problem discussed in this paper possesses an important physical background.