The Viability for Volterra-Type Integral Equations

Viability for Volterra-Type Integral Equations

Abstract

We study viability of closed state constraints for nonlinear Volterra-type integral equations
modeling hereditary (memory) effects. We introduce a history-aware Euler--Volterra approximation
that preserves the nonlocal structure of the dynamics and use it to derive a tangency criterion
ensuring viability of cylindrical constraint sets. Under continuity assumptions, the tangency
condition admits a checkable form through the diagonal kernel term $F(t,t,\cdot)$.