### Abstract

Original language | English |
---|---|

Pages (from-to) | 2185-2228 |

Number of pages | 44 |

Journal | MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES |

Volume | 27 |

Issue number | 12 |

DOIs | |

Publication status | Published - 2017 |

Externally published | Yes |

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### Cite this

*MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES*,

*27*(12), 2185-2228. https://doi.org/10.1142/s0218202517500427

}

*MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES*, vol. 27, no. 12, pp. 2185-2228. https://doi.org/10.1142/s0218202517500427

**Long-Time behavior for crystal dislocation dynamics.** / Patrizi, S.; Valdinoci, E.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Long-Time behavior for crystal dislocation dynamics

AU - Patrizi, S.

AU - Valdinoci, E.

PY - 2017

Y1 - 2017

N2 - We describe the asymptotic states for the solutions of a nonlocal equation of evolutionary type, which have the physical meaning of the atom dislocation function in a periodic crystal. More precisely, we can describe accurately the "smoothing effect" on the dislocation function occurring slightly after a "particle collision" (roughly speaking, two opposite transitions layers average out) and, in this way, we can trap the atom dislocation function between a superposition of transition layers which, as time flows, approaches either a constant function or a single heteroclinic (depending on the algebraic properties of the orientations of the initial transition layers). The results are endowed with explicit and quantitative estimates and, as a byproduct, we show that the ODE systems of particles that govern the evolution of the transition layers does not admit stationary solutions (i.e. roughly speaking, transition layers always move).

AB - We describe the asymptotic states for the solutions of a nonlocal equation of evolutionary type, which have the physical meaning of the atom dislocation function in a periodic crystal. More precisely, we can describe accurately the "smoothing effect" on the dislocation function occurring slightly after a "particle collision" (roughly speaking, two opposite transitions layers average out) and, in this way, we can trap the atom dislocation function between a superposition of transition layers which, as time flows, approaches either a constant function or a single heteroclinic (depending on the algebraic properties of the orientations of the initial transition layers). The results are endowed with explicit and quantitative estimates and, as a byproduct, we show that the ODE systems of particles that govern the evolution of the transition layers does not admit stationary solutions (i.e. roughly speaking, transition layers always move).

UR - https://www.scopus.com/inward/record.uri?eid=2-s2.0-85028353016&doi=10.1142%2fS0218202517500427&partnerID=40&md5=dc1daed14f4a6fb071550f2566837e42

U2 - 10.1142/s0218202517500427

DO - 10.1142/s0218202517500427

M3 - Article

VL - 27

SP - 2185

EP - 2228

JO - MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES

JF - MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES

SN - 0218-2025

IS - 12

ER -