On the existence of a solution for an adsorption dynamic model with the Langmuir isotherm
José R. Fernández, M.C. Muñiz, Cristina Núñez · European Journal of Applied Mathematics · 2014
In this paper, we study an adsorption model arising in the dynamics of several surfactants at the air-water interface, where the Langmuir isotherm is employed for modelling the time-dependent surface concentration, providing a nonlinear dynamical boundary condition. Existence of a weak solution is proved by using the Rothe method for a semi-discrete problem in time. After obtaining somea prioriestimates and passing to the limit in the time discretization parameter, we conclude that the original Langmuir problem has a bounded solution. An uniqueness result is also given.