Solutions to Second-Order Nonlocal Evolution Equations Governed by Non-Autonomous Forms

Abstract

Our main contributions include proving sufficient conditions for the existence of solution to a second order problem with nonzero nonlocal initial conditions, and providing a comprehensive analysis using fundamental solutions and fixed-point techniques. The theoretical results are illustrated through applications to partial differential equations, including vibrating viscoelastic membranes with time-dependent material properties and nonlocal memory effects.

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