Homogenization of a one-dimensional diffusion - discrete absorption equation with feedback

Abstract

The paper is devoted to the diffusion equation with discrete absorption described by a sum of Dirac -functions. Their supports are located at the nodes of some regular grid with the distance between them determined by the integral of solution. This model describes contraction of biological tissue when cells consume some substance influencing their interaction. In the one-dimensional formulation we prove existence of solutions of the discrete problem and their convergence to the solution of the limiting homogenized problem.

Keywords:

• Diffusion-discrete absorption equation with feedback
• existence of solution
• homogenization

AMS Subject Classifications:

• 35B27
• 35Q53
• 35C20

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work was financially supported by the French–Russian PICS BIOMAT CNRS-RFBR grant.