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SPATIALLY NON-UNIFORMAL STATIONARY SOLUTIONS IN A MODEL OF ELECTROCHEMICAL DIFFUSIVE LAYER Savenkova N.P., Kuzmin R.N. 1, Shobukhov A.V. Lomonosov Moscow State University, Faculty of Comput. Mathem. and Cybernetics, Russia 119991, Moscow, Leninskiye Gory, MSU, 2-nd Educ.Build., room 728 phone: +7 (495) 939-52-55, e-mail: shobukhov@cs.msu.su Lomonosov Moscow State University, Faculty of Physics, Russia 119991, Moscow, Leninskiye Gory, MSU, House 1, Build.2 We study a mathematical model of electrochemical processes that take place at the cathode and in the adjacent electrolyte diffusive layer [1]. The transport of positive ions [2] that discharge at the cathode after adsorption, is considered: c c zF c (t , x) = D + (t , ) = 0; c(t , x) ; t x x RT x x
F 2 (t , x) = - c(t , x); (t ,0) = 0 ; (t , ) = 0; 2 0 x x d (t ) = k a c(t ,0) (1 - ) 2 - k d - k e . dt
1

We prove that this model possesses a family of stationary solutions (c*,*,*): 1 c * ( x) = c * (0) 1 + tg 2 c * (0) x ; * ( x) = 0 - ln1 + tg 2 c * (0) x ; 2 2 zF zF 0 = k a c * (0) (1 - *) 2 - (k d + k e ) *; = ; = . RT 0 Linearization of the original system in the vicinity of (c*,*,*) makes it possible to find the stability conditions for these spatially non-uniformal time-invariant solutions. . 1. Koper M.T.M., Sluyters J.H. Instabilities and oscillations in simple models of electrocatalytic surface reactions. // Journal of Electroanalytical Chemistry, v.371, 1994. pp.149-159. 2. Damaskin B.B., Petrii O.A., Tsirlina G.A. Electrochemistry. (in Russ.) - M.:, 2006. 672 p.