Hyperbolic non-conserved phase field equations

Horacio G. Rotstein; Alexander Nepomnyashchy; Amy Novick-Cohen

doi:10.1016/S0022-0248(98)01008-2

Hyperbolic non-conserved phase field equations

Horacio G. Rotstein
, Alexander Nepomnyashchy
, Amy Novick-Cohen

Research output: Contribution to journal › Conference article › peer-review

4 Scopus citations

Abstract

We consider the following hyperbolic system of PDEs which generalize the classical phase field equations with a non-conserved order parameter φ and temperature u: u_tt + ε²φ_tt + γ₁u_t + ε²γ₁φ_t = αΔu, ε²φ_tt + γ₂ε²φ_t = ε²Δφ + f(φ) + εu for ε≪1. We present the model, derive a law for the evolution of the interface which generalizes the classical flow by mean curvature equation, and analyze the evolution of some simply shaped interfaces.

Original language	English (US)
Pages (from-to)	1262-1266
Number of pages	5
Journal	Journal of Crystal Growth
Volume	198-199
Issue number	pt 2
DOIs	https://doi.org/10.1016/S0022-0248(98)01008-2
State	Published - Mar 1999
Externally published	Yes
Event	Proceedings of the 1998 10th International Conference on Vapor Growth and Epitaxy and Specialist Workshops on Crystal Growth, ICVGE-10 - Jerusalem, Isr Duration: Jul 26 1998 → Jul 31 1998

All Science Journal Classification (ASJC) codes

Condensed Matter Physics
Inorganic Chemistry
Materials Chemistry

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10.1016/S0022-0248(98)01008-2

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@article{c13542a754af4a0d99b7daac776277f1,

title = "Hyperbolic non-conserved phase field equations",

abstract = "We consider the following hyperbolic system of PDEs which generalize the classical phase field equations with a non-conserved order parameter φ and temperature u: utt + ε2φtt + γ1ut + ε2γ1φt = αΔu, ε2φtt + γ2ε2φt = ε2Δφ + f(φ) + εu for ε≪1. We present the model, derive a law for the evolution of the interface which generalizes the classical flow by mean curvature equation, and analyze the evolution of some simply shaped interfaces.",

author = "Rotstein, \{Horacio G.\} and Alexander Nepomnyashchy and Amy Novick-Cohen",

year = "1999",

month = mar,

doi = "10.1016/S0022-0248(98)01008-2",

language = "English (US)",

volume = "198-199",

pages = "1262--1266",

journal = "Journal of Crystal Growth",

issn = "0022-0248",

publisher = "Elsevier B.V.",

number = "pt 2",

note = "Proceedings of the 1998 10th International Conference on Vapor Growth and Epitaxy and Specialist Workshops on Crystal Growth, ICVGE-10 ; Conference date: 26-07-1998 Through 31-07-1998",

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TY - JOUR

T1 - Hyperbolic non-conserved phase field equations

AU - Rotstein, Horacio G.

AU - Nepomnyashchy, Alexander

AU - Novick-Cohen, Amy

PY - 1999/3

Y1 - 1999/3

N2 - We consider the following hyperbolic system of PDEs which generalize the classical phase field equations with a non-conserved order parameter φ and temperature u: utt + ε2φtt + γ1ut + ε2γ1φt = αΔu, ε2φtt + γ2ε2φt = ε2Δφ + f(φ) + εu for ε≪1. We present the model, derive a law for the evolution of the interface which generalizes the classical flow by mean curvature equation, and analyze the evolution of some simply shaped interfaces.

AB - We consider the following hyperbolic system of PDEs which generalize the classical phase field equations with a non-conserved order parameter φ and temperature u: utt + ε2φtt + γ1ut + ε2γ1φt = αΔu, ε2φtt + γ2ε2φt = ε2Δφ + f(φ) + εu for ε≪1. We present the model, derive a law for the evolution of the interface which generalizes the classical flow by mean curvature equation, and analyze the evolution of some simply shaped interfaces.

UR - https://www.scopus.com/pages/publications/0033514535

UR - https://www.scopus.com/pages/publications/0033514535#tab=citedBy

U2 - 10.1016/S0022-0248(98)01008-2

DO - 10.1016/S0022-0248(98)01008-2

M3 - Conference article

AN - SCOPUS:0033514535

SN - 0022-0248

VL - 198-199

SP - 1262

EP - 1266

JO - Journal of Crystal Growth

JF - Journal of Crystal Growth

IS - pt 2

T2 - Proceedings of the 1998 10th International Conference on Vapor Growth and Epitaxy and Specialist Workshops on Crystal Growth, ICVGE-10

Y2 - 26 July 1998 through 31 July 1998

ER -

Hyperbolic non-conserved phase field equations

Abstract

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