Further spectral properties of uniformly elliptic operators that include a non-local term

被引：5
作者：
Dodds, Niall [1 ]
机构：
[1] Univ Dundee, Div Math, Dundee DD1 4HN, Scotland
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2008年 / 197卷 / 01期
关键词：
non-local; uniformly elliptic; eigenvalues; integro-differential;
D O I：
10.1016/j.amc.2007.07.049
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we consider the eigenvalues of a class of non-local differential operators. The real eigenvalues of certain examples of these operators have previously been plotted ( as functions of a fundamental parameter in the operator), using appropriate computer software. Here we show how the complex eigenvalues of such operators may also be plotted. We use the plots of both the real and the complex eigenvalues to motivate a number of new theoretical results regarding the structure of the spectrum, which we subsequently prove under suitable hypotheses. (C) 2007 Elsevier Inc. All rights reserved.
引用
收藏
页码：317 / 327
页数：11
相关论文
共 20 条
[11]   A NONLOCAL STURM-LIOUVILLE EIGENVALUE PROBLEM [J].
FREITAS, P .
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 1994, 124 :169-188
[12]   Positivity results for a nonlocal elliptic equation [J].
Freitas, P ;
Sweers, G .
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 1998, 128 :697-715
[13]   STATIONARY SOLUTIONS OF AN EQUATION MODELING OHMIC HEATING [J].
FREITAS, P ;
GRINFELD, M .
APPLIED MATHEMATICS LETTERS, 1994, 7 (03) :1-6
[14]  
Freitas P., 2000, DIFFERENTIAL INTEGRA, V13, P265
[15]   LOCAL VS NON-LOCAL INTERACTIONS IN POPULATION-DYNAMICS [J].
FURTER, J ;
GRINFELD, M .
JOURNAL OF MATHEMATICAL BIOLOGY, 1989, 27 (01) :65-80
[16]  
Henry D., 1981, Geometric Theory of Semilinear Parabolic Partial Differential Equations, DOI [DOI 10.1007/BFB0089647, 10.1007/BFb0089647]
[17]   Global existence and divergence of critical solutions of a non-local parabolic problem in Ohmic heating process [J].
Kavallaris, NI ;
Lacey, AA ;
Tzanetis, DE .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2004, 58 (7-8) :787-812
[18]   Hot spot formation in microwave heated ceramic fibres [J].
Kriegsmann, GA .
IMA JOURNAL OF APPLIED MATHEMATICS, 1997, 59 (02) :123-148
[19]  
Lacey A., 1995, Eur. J. Appl. Math., V6, P127, DOI 10.1017/S095679250000173X
[20]   BLOWING-UP OF SOLUTION FOR A NONLOCAL REACTION-DIFFUSION PROBLEM IN COMBUSTION THEORY [J].
PAO, CV .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1992, 166 (02) :591-600
12