Publication 22-CNA-016

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

Amit Acharya
Dept. of Civil & Environmental Engineering
Center for Nonlinear Analysis
Carnegie Mellon University
Pittsburgh, PA 15213
acharyaamit@cmu.edu

Marshall Slemrod
Department of Mathematics
University of Wisconsin
Madison, WI 53706
slemrod@math.wisc.edu

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.

This paper is dedicated to our friend Costas Dafermos on the occasion of his 80th birthday.

Get the paper in its entirety as  22-CNA-016.pdf

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