On an Equation From the Theory of Field Dislocation Mechanics

Amit Acharya; Luc Tartar

Bollettino dell'Unione Matematica Italiana (2011)

  • Volume: 4, Issue: 3, page 409-444
  • ISSN: 0392-4041

Abstract

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Global existence and uniqueness results for a quasilinear system of partial differential equations in one space dimension and time representing the transport of dislocation density are obtained. Stationary solutions of the system are also studied, and an infinite dimensional class of equilibria is derived. These time (in)dependent solutions include both periodic and aperiodic spatial distributions of smooth fronts of plastic distortion representing dislocation twist boundary microstructure. Dominated by hyperbolic transport-like features and at the same time containing a large class of equilibria, our system differs qualitatively from regularized systems of hyperbolic conservation laws and neither does it fit into a gradient flow structure.

How to cite

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Acharya, Amit, and Tartar, Luc. "On an Equation From the Theory of Field Dislocation Mechanics." Bollettino dell'Unione Matematica Italiana 4.3 (2011): 409-444. <http://eudml.org/doc/290710>.

@article{Acharya2011,
abstract = {Global existence and uniqueness results for a quasilinear system of partial differential equations in one space dimension and time representing the transport of dislocation density are obtained. Stationary solutions of the system are also studied, and an infinite dimensional class of equilibria is derived. These time (in)dependent solutions include both periodic and aperiodic spatial distributions of smooth fronts of plastic distortion representing dislocation twist boundary microstructure. Dominated by hyperbolic transport-like features and at the same time containing a large class of equilibria, our system differs qualitatively from regularized systems of hyperbolic conservation laws and neither does it fit into a gradient flow structure.},
author = {Acharya, Amit, Tartar, Luc},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {409-444},
publisher = {Unione Matematica Italiana},
title = {On an Equation From the Theory of Field Dislocation Mechanics},
url = {http://eudml.org/doc/290710},
volume = {4},
year = {2011},
}

TY - JOUR
AU - Acharya, Amit
AU - Tartar, Luc
TI - On an Equation From the Theory of Field Dislocation Mechanics
JO - Bollettino dell'Unione Matematica Italiana
DA - 2011/10//
PB - Unione Matematica Italiana
VL - 4
IS - 3
SP - 409
EP - 444
AB - Global existence and uniqueness results for a quasilinear system of partial differential equations in one space dimension and time representing the transport of dislocation density are obtained. Stationary solutions of the system are also studied, and an infinite dimensional class of equilibria is derived. These time (in)dependent solutions include both periodic and aperiodic spatial distributions of smooth fronts of plastic distortion representing dislocation twist boundary microstructure. Dominated by hyperbolic transport-like features and at the same time containing a large class of equilibria, our system differs qualitatively from regularized systems of hyperbolic conservation laws and neither does it fit into a gradient flow structure.
LA - eng
UR - http://eudml.org/doc/290710
ER -

References

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