Abstract
In this paper we study a new multidimensional mixed-kinetic adsorption model which consists of a nonlinear evolution system of two parabolic partial differential equations: a convective diffusion equation for the bulk surfactant concentration in a bounded domain and a surface diffusion equation for its surface concentration on a compact Lipschitz manifold. The two equations are coupled with a nonlinear relationship, consistent with the Langmuir--Hinshelwood model, which describes the adsorption-desorption transport of surfactant molecules between the bulk phase and one part of its boundary. We provide results on the unique weak solvability of the system and non-negativity of its solution. We use the truncation method combined with the fixed point approach and the theory of time-dependent partial differential equations on manifolds.
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