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arXiv · 2510.25881

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

Sajid Ullah·Vittorio Colao
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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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Sajid Ullah, Vittorio Colao. 2025-10-29. Solutions to Second-Order Nonlocal Evolution Equations Governed by Non-Autonomous Forms. https://doi.org/10.7494/opmath.202603081

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