Morphological spatial patterns in a reaction diffusion model for metal growth
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1.
Dipartimento di Ingegneria dell’Innovazione, Università del Salento - Lecce, via per Monteroni, I-73100 Lecce
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2.
Dipartimento di Scienze Motorie e della Salute, Università di Cassino, Campus Folcara, Loc. S.Angelo, I-03043 Cassino
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3.
Dipartimento di Matematica, Università del Salento - Lecce, via per Arnesano, I-73100 Lecce
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Received:
01 May 2009
Accepted:
29 June 2018
Published:
01 April 2010
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MSC :
35K57, 62P30, 65M.
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In this paper a reaction-diffusion system modelling metal growth processes is considered, to investigate -
within the electrodeposition context- the formation of morphological patterns in a finite two-dimensional spatial
domain. Nonlinear dynamics of the system is studied from both the analytical and numerical points of view. Phase-space
analysis is provided and initiation of spatial patterns induced by diffusion is shown to occur in a suitable region of
the parameter space. Investigations aimed at establishing the role of some relevant chemical parameters on stability
and selection of solutions are also provided. By the numerical approximation of the equations, simulations are
presented which turn out to be in good agreement with experiments for the electrodeposition of Au-Cu and Au-Cu-Cd
alloys.
Citation: Benedetto Bozzini, Deborah Lacitignola, Ivonne Sgura. Morphological spatial patterns in a reaction diffusion model for metal growth[J]. Mathematical Biosciences and Engineering, 2010, 7(2): 237-258. doi: 10.3934/mbe.2010.7.237
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Abstract
In this paper a reaction-diffusion system modelling metal growth processes is considered, to investigate -
within the electrodeposition context- the formation of morphological patterns in a finite two-dimensional spatial
domain. Nonlinear dynamics of the system is studied from both the analytical and numerical points of view. Phase-space
analysis is provided and initiation of spatial patterns induced by diffusion is shown to occur in a suitable region of
the parameter space. Investigations aimed at establishing the role of some relevant chemical parameters on stability
and selection of solutions are also provided. By the numerical approximation of the equations, simulations are
presented which turn out to be in good agreement with experiments for the electrodeposition of Au-Cu and Au-Cu-Cd
alloys.
References
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