What question did this study set out to answer?

The aim is to explore solvability, stability, and regularity of nonlocal pseudo-parabolic equations with time delays.

May 21, 2026

On regularity and stability for nonlocal pseudo-parabolic equations involving time-varying delays

Key Points

The aim is to explore solvability, stability, and regularity of nonlocal pseudo-parabolic equations with time delays.
Analyzes the class of nonlocal pseudo-parabolic equations with Sonine kernels and time-varying delays
Employs regularity estimates of resolvents and a nonlocal Halanay inequality
Uses fixed point arguments and fractional Sobolev spaces for analysis
Proves the Hölder regularity of mild solutions to the equations
Demonstrates convergence of solutions to corresponding subdiffusion equations

Abstract

We study a class of nonlocal pseudo-parabolic equations with Sonine kernels, where the nonlinearity involves time-varying delays. Our main goal is to address some qualitative questions including the solvability, stability and the Hölder regularity for mild solutions. In addition, we show a result on the convergence of solutions to ones of corresponding subdiffusion equations. The main ingredients for our analysis are regularity estimates of resolvents, a nonlocal Halanay inequality, the fixed point argument and the embedding of fractional Sobolev spaces.

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