A neumann boundary value problem in two-ion electro-diffusion with unequal valencies

• Autores: Amster, P.; Kwong, M.K.; Rogers, C.
• Año de publicación: 2012
• Idioma: inglés
• Tipo de recurso: artículo
• Fuente: Discrete Contin. Dyn. Syst. Ser. B 2012;17(7):2299-2311
• Materia: Neumann boundary conditions; Topological index; Two-ion electro-diffusion; Unequal valencies
• Institución: Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales

In prior work, a series of two-point boundary value problems have been investigated for a steady state two-ion electro-diffusion model system in which the sum of the valencies ν + and ν - is zero. In that case, reduction is obtained to the canonical Painlevé II equation for the scaled electric field. Here, a physically important Neumann boundary value problem in the generic case when ν ++ν - = 0 is investigated. The problem is novel in that the model equation for the electric field involves yet to be determined boundary values of the solution. A reduction of the Neumann boundary value problem in terms of elliptic functions is obtained for privileged valency ratios. A topological index argument is used to establish the existence of a solution in the general case, under the assumption ν ++ν - ≤ 0.
Fil:Amster, P. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.