Qualitative analysis of a delayed non-Fickian model

Abstract

This article focusses on the mathematical analysis of a delayed integro-differential model in which flux does not obey the classical Fick's law. The well-posedness of the integro-differential model in the Hadamard's sense is established. The dependence on the delay parameter of the total amount of desorpted/sorpted mass is studied. Numerical results that show the effectiveness of the model are included.

Keywords:

• Fick's law
• non-Fickian flux
• delayed integro-differential equation
• well-posedness in Hadamard sense
• sorption
• desorption

AMS Classifications:

• 35B35
• 35B40
• 35C10
• 35K65

Acknowledgement

This work was partially supported by Project:PTDC/MAT/74548/2006.