Nonlocal eigenvalue problems arising in a generalized phase-field-type system

Nonlocal eigenvalue problems arising in a generalized phase-field-type system
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广义相场型系统中出现的非局部特征值问题

DOI：
10.1007/s13160-017-0254-z
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发表时间：
2018
期刊：
Japan J. Indust. Appl. Math.
影响因子：
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通讯作者：
S. Jimbo and Y. Morita
S. Jimbo and Y. Morita
中科院分区：
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文献类型：
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作者：
N. Jovanovic;F. Martinache;O. Guyon;C. Clergeon;G. Singh;T. Kudo;V. Garrel;K. Newman;D. Doughty;J. Lozi;J. Males;Y. Minowa;Y. Hayano;N. Takato;J. Morino;J. Kuhn;E. Serabyn;B. Norris;P. Tuthill;G. Schworer;P. Stewart;L. Close;E. Huby,;Kishi Tatsuro;S. Jimbo and Y. Morita

文献摘要

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我们讨论了一个广义相场型系统，它是由具有守恒律的反应扩散方程组变换而成的。我们考虑定常问题，将其归结为一个带非局部项的标量椭圆型方程，并研究了线性化的特征值问题。我们首先用谱比较方法证明了该问题的不稳定本征值的个数与原系统的线性化特征值问题的不稳定本征值个数一致。接下来，我们展示了当非局部项的系数趋于无穷大时，标量问题本征值的极限行为。
We deal with a generalized phase-field-type system that arises as a transformed system of reaction-diffusion equations with a conservation law. We consider the stationary problem which is reduced to a scalar elliptic equation with a nonlocal term, and study the linearized eigenvalue problem. We first prove by the spectral comparison argument that the number of unstable eigenvalues for the problem coincides with the one of the linearized eigenvalue problem for the original system. We next show a limiting behavior of eigenvalues for the scalar problem as the coefficient of the nonlocal term goes to infinity.