Solutions to Second-Order Nonlocal Evolution Equations Governed by Non-Autonomous Forms
Analysis of PDEs
2026-05-06 v1
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.
Keywords
Cite
@article{arxiv.2510.25881,
title = {Solutions to Second-Order Nonlocal Evolution Equations Governed by Non-Autonomous Forms},
author = {Sajid Ullah and Vittorio Colao},
journal= {arXiv preprint arXiv:2510.25881},
year = {2026}
}
Comments
27