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Abstract:

Existence, uniqueness, and multiplicity properties are established via a variational formulation for a Painlevé II model subject to radiation boundary conditions in two-ion electrodiffusion. Numerical experiments using an adapted shooting method are also presented to support the theoretical results. © 2013 Elsevier Ltd. All rights reserved.

Registro:

Documento: Artículo
Título:A Painlevé II model in two-ion electrodiffusion with radiation boundary conditions
Autor:Amster, P.; Kwong, M.K.; Rogers, C.
Filiación:Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Argentina
IMAS-CONICET, Argentina
Department of Applied Mathematics, Hong Kong Polytechnic University, Hunghom, Kowloon, Hong Kong
Australian Research Council Centre of Excellence for Mathematics and Statistics of Complex Systems, School of Mathematics, University of New South Wales, Sydney, NSW 2052, Australia
Idioma: Inglés
Palabras clave:Electrodiffusion; Numerical experiments; Painleve; Radiation boundary condition; Shooting methods; Variational formulation; Boundary conditions; Numerical methods; Diffusion
Año:2014
Volumen:16
Número:1
Página de inicio:120
Página de fin:131
DOI: http://dx.doi.org/10.1016/j.nonrwa.2013.09.011
Título revista:Nonlinear Analysis: Real World Applications
Título revista abreviado:Nonlinear Anal. Real World Appl.
ISSN:14681218
Registro:http://digital.bl.fcen.uba.ar/collection/paper/document/paper_14681218_v16_n1_p120_Amster

Referencias:

  • Grafov, B.M., Chernenko, A.A., Theory of the passage of a constant current through a solution of a binary electrolyte (1962) Dokl. Akad. Nauk SSR, 146, p. 135
  • Bass, L., Electric structures of interfaces in steady electrolysis (1964) Trans. Faraday Soc., 60, pp. 1656-1663
  • Volgin, V.M., Davydov, A.D., Ionic transport through ion-exchange and bipolar membranes (2005) J. Mombrane Sci., 259, pp. 110-121
  • Mariani, M.C., Amster, P., Rogers, C., Dirichlet and periodic-type boundary value problems for Painlevé II (2002) J. Math. Anal. Appl., 265, pp. 1-11
  • Amster, P., Mariani, M.C., Rogers, C., Tisdell, C.C., On two-point boundary value problems in multi-ion electrodiffusion (2004) J. Math. Anal. Appl., 289, pp. 712-721
  • Amster, P., Rogers, C., On boundary value problems in three-ion electrodiffusion (2007) J. Math. Anal. Appl., 333, pp. 42-51
  • De Coster, C., Habets, P., Two-point boundary value problems: Lower and upper solutions (2006) Mathematics in Science and Engineering, 205. , Elsevier Amsterdam
  • Amster, P., Vicchi, L., Rogers, C., Boundary value problems on the half-line for a generalised Painlevé II equation (2009) Nonlinear Anal., 71, pp. 149-154
  • Amster, P., Kwong, M.K., Rogers, C., On a Neumann boundary value problem for the Painlevé II equation in two-ion electro-diffusion (2011) Nonlinear Anal., 74, pp. 2897-2907
  • Amster, P., Kwong, M.K., Rogers, C., A Neumann boundary value problem in two-ion electro-diffusion with unequal valencies (2012) Discrete Contin. Dyn. Syst. Ser. B, 17, pp. 2299-2311
  • Rogers, C., Bassom, A.P., Schief, W.K., On a Painlevé II model in steady electrolysis: Application of a Bäcklund transformation (1999) J. Math. Anal. Appl., 240, pp. 367-381
  • Bass, L.K., Nimmo, J., Rogers, C., Schief, W.K., Electrical structures of interfaces. A Painlevé II model (2010) Proc. R. Soc. A., 466, pp. 2117-2136
  • Bracken, A.J., Bass, L., Rogers, C., Bäcklund flux-quantization in a model of electrodiffusion based on Painlevé II (2012) J. Phys. A., 45, pp. 105-204
  • Mawhin, J., Willem, M., (1989) Critical Point Theory and Hamiltonian Systems, , Springer-Verlag New York
  • Rabinowitz, P., Some minimax theorems and applications to partial differential equations (1978) Nonlinear Analysis: A Collection of Papers in Honor of Erich Röthe, pp. 161-177. , Academic Press NY

Citas:

---------- APA ----------
Amster, P., Kwong, M.K. & Rogers, C. (2014) . A Painlevé II model in two-ion electrodiffusion with radiation boundary conditions. Nonlinear Analysis: Real World Applications, 16(1), 120-131.
http://dx.doi.org/10.1016/j.nonrwa.2013.09.011
---------- CHICAGO ----------
Amster, P., Kwong, M.K., Rogers, C. "A Painlevé II model in two-ion electrodiffusion with radiation boundary conditions" . Nonlinear Analysis: Real World Applications 16, no. 1 (2014) : 120-131.
http://dx.doi.org/10.1016/j.nonrwa.2013.09.011
---------- MLA ----------
Amster, P., Kwong, M.K., Rogers, C. "A Painlevé II model in two-ion electrodiffusion with radiation boundary conditions" . Nonlinear Analysis: Real World Applications, vol. 16, no. 1, 2014, pp. 120-131.
http://dx.doi.org/10.1016/j.nonrwa.2013.09.011
---------- VANCOUVER ----------
Amster, P., Kwong, M.K., Rogers, C. A Painlevé II model in two-ion electrodiffusion with radiation boundary conditions. Nonlinear Anal. Real World Appl. 2014;16(1):120-131.
http://dx.doi.org/10.1016/j.nonrwa.2013.09.011