Homogenization of the Dirac-like system

Jiann Sheng Jiang; Chi Kun Lin

doi:10.1142/S0218202501000921

Homogenization of the Dirac-like system

Jiann Sheng Jiang^*, Chi Kun Lin

^*Corresponding author for this work

National Cheng Kung University

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

Abstract

The homogenization of the Dirac-like system is studied. It generates memory effects. The memory (or nonlocal) kernel is described by the Volterra integral equation. When the coefficient is independent of time, the memory kernel can be characterized explicitly in terms of Young's measure. The homogenized equation can be reformulated in the kinetic form by introducing the kinetic variable. We also characterize the memory kernel when the coefficient is of separable variable.

Original language	English
Pages (from-to)	433-458
Number of pages	26
Journal	Mathematical Models and Methods in Applied Sciences
Volume	11
Issue number	3
DOIs	https://doi.org/10.1142/S0218202501000921
Publication status	Published - Apr 2001
Externally published	Yes

Keywords

Dirac-like system
Dunford-Taylor integral
Hergoltz function
Homogenization
Kinetic formulation
Volterra integral equation
Weak limits
Young's measure

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10.1142/S0218202501000921

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title = "Homogenization of the Dirac-like system",

abstract = "The homogenization of the Dirac-like system is studied. It generates memory effects. The memory (or nonlocal) kernel is described by the Volterra integral equation. When the coefficient is independent of time, the memory kernel can be characterized explicitly in terms of Young's measure. The homogenized equation can be reformulated in the kinetic form by introducing the kinetic variable. We also characterize the memory kernel when the coefficient is of separable variable.",

keywords = "Dirac-like system, Dunford-Taylor integral, Hergoltz function, Homogenization, Kinetic formulation, Volterra integral equation, Weak limits, Young's measure",

author = "Jiang, {Jiann Sheng} and Lin, {Chi Kun}",

note = "Funding Information: This work was partial supported by the National Science Council of Taiwan under NSC89-2115-M-006-006.",

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AU - Jiang, Jiann Sheng

AU - Lin, Chi Kun

N1 - Funding Information: This work was partial supported by the National Science Council of Taiwan under NSC89-2115-M-006-006.

PY - 2001/4

Y1 - 2001/4

N2 - The homogenization of the Dirac-like system is studied. It generates memory effects. The memory (or nonlocal) kernel is described by the Volterra integral equation. When the coefficient is independent of time, the memory kernel can be characterized explicitly in terms of Young's measure. The homogenized equation can be reformulated in the kinetic form by introducing the kinetic variable. We also characterize the memory kernel when the coefficient is of separable variable.

AB - The homogenization of the Dirac-like system is studied. It generates memory effects. The memory (or nonlocal) kernel is described by the Volterra integral equation. When the coefficient is independent of time, the memory kernel can be characterized explicitly in terms of Young's measure. The homogenized equation can be reformulated in the kinetic form by introducing the kinetic variable. We also characterize the memory kernel when the coefficient is of separable variable.

KW - Dirac-like system

KW - Dunford-Taylor integral

KW - Hergoltz function

KW - Homogenization

KW - Kinetic formulation

KW - Volterra integral equation

KW - Weak limits

KW - Young's measure

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DO - 10.1142/S0218202501000921

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SP - 433

EP - 458

JO - Mathematical Models and Methods in Applied Sciences

JF - Mathematical Models and Methods in Applied Sciences

IS - 3

ER -

Homogenization of the Dirac-like system

Abstract

Keywords

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