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On the existence of a solution for an adsorption dynamic model with the Langmuir isotherm

Published online by Cambridge University Press:  30 July 2014

J. R. FERNÁNDEZ ,
M. C. MUÑIZ  and
C. NÚÑEZ
J. R. FERNÁNDEZ
Affiliation:
Departamento de Matemática Aplicada I, Universidade de Vigo, ETSI Telecomunicación, Campus As Lagoas Marcosende s/n, 36310 Vigo, Spain email: jose.fernandez@uvigo.es
M. C. MUÑIZ
Affiliation:
Departamento de Matemática Aplicada, Universidade de Santiago de Compostela, Facultade de Matemáticas, Campus Vida s/n, 15782 Santiago de Compostela, Spain email: mcarmen.muniz@usc.es
C. NÚÑEZ
Affiliation:
Departamento de Didáctica de las Ciencias Experimentales, Facultad de Ciencias de la Educación, Campus Norte, 15782 Santiago de Compostela, Spain email: cristina.nunez.garcia@usc.es
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Abstract

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 some a priori estimates 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.

Keywords

76T1076A2076M2076M3092C45

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Type
Papers
Information
European Journal of Applied Mathematics , Volume 25 , Issue 5 , October 2014 , pp. 629 - 653
Copyright
Copyright © Cambridge University Press 2014 

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