Original scientific paper

https://doi.org/10.21857/ydkx2c3rp9

Shadow limit for parabolic-ODE systems through a cut-off argument

Anna Marciniak-Czochra ; Institute of Applied Mathematics, IWR and BIOQUANT, University of Heidelberg, Im Neuenheimer Feld 267, 69120 Heidelberg, Germany
Andro Mikelić orcid.org/0000-0002-4752-8705 ; Univ Lyon, Université Claude Bernard Lyon 1, CNRS UMR 5208, Institut Camille Jordan, 43 blvd. du 11 novembre 1918, F-69622 Villeurbanne cedex, France

Abstract

We study a shadow limit (the infinite diffusion coefficient-limit) of a system of ODEs coupled with a diagonal system of semilinear heat equations in a bounded domain with homogeneous Neumann boundary conditions. The recent convergence proof by the energy approach from [19], developed for the case of a single PDE, is revisited and generalized to the case of the coupled system. Furthermore, we give a new convergence proof relying on the introduction of a well-prepared related cut-off system and on a construction of the barrier functions and comparison test functions, new in the literature. It leads to the L∞-estimates proportional to the inverse of the diffusion coefficient.

Keywords

Shadow limit; reaction-diffusion equations; model reduction

Hrčak ID:

186433

URI

https://hrcak.srce.hr/186433

Publication date:

13.9.2017.

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