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LONG TIME BEHAVIOR OF DYNAMIC SOLUTION TO PEIERLS–NABARRO DISLOCATION MODEL

Publication ,  Journal Article
Gao, Y; Liu, JG
Published in: Methods and Applications of Analysis
January 1, 2020
Published version (DOI)

In this paper we study the relaxation process of the Peierls-Nabarro dislocation model, which is a gradient flow with a singular nonlocal energy and a double well potential describing how the materials relax to its equilibrium with the presence of a dislocation. We prove the dynamic solution to the Peierls-Nabarro model will converge exponentially to a shifted steady profile which is uniquely determined.

Duke Scholars

Jian-Guo Liu
Author Jian-Guo Liu Physics

Published In

Methods and Applications of Analysis

DOI

10.4310/MAA.2020.v27.n2.a4

EISSN

1945-0001

ISSN

1073-2772

Publication Date

January 1, 2020

Volume

27

Issue

2

Start / End Page

161 / 198

Related Subject Headings

  • 4904 Pure mathematics
  • 4902 Mathematical physics
  • 4901 Applied mathematics
  • 0105 Mathematical Physics
  • 0102 Applied Mathematics
  • 0101 Pure Mathematics
 

Citation

APA
Chicago
ICMJE
MLA
NLM
Gao, Y., & Liu, J. G. (2020). LONG TIME BEHAVIOR OF DYNAMIC SOLUTION TO PEIERLS–NABARRO DISLOCATION MODEL. Methods and Applications of Analysis, 27(2), 161–198. https://doi.org/10.4310/MAA.2020.v27.n2.a4
Gao, Y., and J. G. Liu. “LONG TIME BEHAVIOR OF DYNAMIC SOLUTION TO PEIERLS–NABARRO DISLOCATION MODEL.” Methods and Applications of Analysis 27, no. 2 (January 1, 2020): 161–98. https://doi.org/10.4310/MAA.2020.v27.n2.a4.
Gao Y, Liu JG. LONG TIME BEHAVIOR OF DYNAMIC SOLUTION TO PEIERLS–NABARRO DISLOCATION MODEL. Methods and Applications of Analysis. 2020 Jan 1;27(2):161–98.
Gao, Y., and J. G. Liu. “LONG TIME BEHAVIOR OF DYNAMIC SOLUTION TO PEIERLS–NABARRO DISLOCATION MODEL.” Methods and Applications of Analysis, vol. 27, no. 2, Jan. 2020, pp. 161–98. Scopus, doi:10.4310/MAA.2020.v27.n2.a4.
Gao Y, Liu JG. LONG TIME BEHAVIOR OF DYNAMIC SOLUTION TO PEIERLS–NABARRO DISLOCATION MODEL. Methods and Applications of Analysis. 2020 Jan 1;27(2):161–198.

Published In

Methods and Applications of Analysis

DOI

10.4310/MAA.2020.v27.n2.a4

EISSN

1945-0001

ISSN

1073-2772

Publication Date

January 1, 2020

Volume

27

Issue

2

Start / End Page

161 / 198

Related Subject Headings

  • 4904 Pure mathematics
  • 4902 Mathematical physics
  • 4901 Applied mathematics
  • 0105 Mathematical Physics
  • 0102 Applied Mathematics
  • 0101 Pure Mathematics