INSTABILITY OF HYSTERETIC PHASE INTERFACES IN A MEAN-FIELD MODEL WITH INHOMOGENEITIES

被引：1

作者：

Herrmann, Michael ^{[1
]}

Niethammer, Barbara ^{[2
]}

机构：

[1] Tech Univ Carolo Wilhelmina Braunschweig, Math, D-38092 Braunschweig, Germany

[2] Univ Bonn, Inst Angew Math, D-53115 Bonn, Germany

来源：

SIAM JOURNAL ON APPLIED MATHEMATICS | 2023年 / 83卷 / 04期

关键词：

hysteretic phase interfaces; instability of traveling waves; rate-independent evolution of particle systems; TRANSITIONS; DYNAMICS; SYSTEMS; VISCOELASTICITY; DISSIPATION; KRAMERS;

D O I：

10.1137/22M153197X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study a system of nonidentical bistable particles that is driven by a dynamical constraint and coupled through a nonlocal mean-field. Assuming piecewise affine constitutive laws we prove the existence of traveling wave solutions and characterize their dynamical stability. Our findings explain the two dynamical regimes for phase interface that can be observed in numerical simulations with different parameters. We further discuss the convergence to a rate-independent model with strong hysteresis in the limit of vanishing relaxation time.

引用

页码：1422 / 1443

页数：22

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