Analysis of evolution equation with variable-exponent memory modeling multiscale viscoelasticity

TL;DR

This paper studies a complex evolution equation modeling multiscale viscoelastic materials with variable memory, establishing well-posedness and solution regularity influenced by variable exponents.

Contribution

It introduces a novel analysis of an evolution equation with variable-exponent memory, proving well-posedness and characterizing solution regularity based on initial conditions.

Findings

Proved well-posedness of the model

Derived weighted solution regularity

Characterized initial singularity effects

Abstract

We investigate the well-posedness and solution regularity of an evolution equation with non-positive type variable-exponent memory, which describes multiscale viscoelasticity in materials with memory. The perturbation method is applied for model transformation, based on which the well-posedness is proved. Then the weighted solution regularity is derived, where the initial singularity is characterized by the initial value of variable exponent.