Existence, uniqueness, and long-time behavior of linearized field dislocation dynamics

TL;DR

This paper analyzes a linearized PDE system modeling dislocation dynamics in crystals, establishing fundamental mathematical properties such as existence, uniqueness, and long-term behavior using semigroup theory.

Contribution

It provides the first rigorous mathematical analysis of the linearized dislocation dynamics system, focusing on existence, uniqueness, and asymptotic behavior.

Findings

Proves existence and uniqueness of solutions.

Characterizes the long-time asymptotic behavior.

Uses linear semigroup theory for analysis.

Abstract

This paper examines a system of partial differential equations describing dislocation dynamics in a crystalline solid. In particular we consider dynamics linearized about a state of zero stress and use linear semigroup theory to establish existence, uniqueness, and time asymptotic behavior of the linear system.