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期刊名称: Applications of Mathematics
Volume:64    Issue:2        Page:169-194
ISSN:0862-7940

Nonuniqueness of implicit lattice Nagumo equation期刊论文

作者: Stehlík Petr Volek Jonáš
DOI:10.21136/AM.2019.0270-18

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页码: 169-194
被引频次: 0
出版者: Springer Berlin Heidelberg,ACAD SCIENCES CZECH REPUBLIC, INST MATHEMATICS,Springer
期刊名称: Applications of Mathematics
ISSN: 0862-7940
卷期: Volume:64    Issue:2
语言: English
摘要: We consider the implicit discretization of Nagumo equation on finite lattices and show that its variational formulation corresponds in various parameter settings to convex, mountain-pass or saddle-point geometries. Consequently, we are able to derive conditions under which the implicit discretization yields multiple solutions. Interestingly, for certain parameters we show nonuniqueness for arbitrarily small discretization steps. Finally, we provide a simple example showing that the nonuniqueness can lead to complex dynamics in which the number of bounded solutions grows exponentially in time iterations, which in turn implies infinite number of global trajectories.
相关主题: nonlinear algebraic problem, 65Q10, lattice differential equation, variational method, Theoretical, Mathematical and Computational Physics, 34A33, Mathematics, 35K57, implicit discretization, Optimization, reaction-diffusion equation, 39A12, Classical and Continuum Physics, Analysis, Mathematical and Computational Engineering, Applications of Mathematics, MATHEMATICS, APPLIED, DIFFUSION, TRAVELING-WAVES, Lattice theory, Research, Variational principles, Mathematical research, Differential equations,

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