Shadow limit for parabolic-ODE systems through a cut-off argument
We study a shadow limit (the infinite diffusion coefficientlimit) 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...
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| Hauptverfasser: | , |
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| Dokumenttyp: | Article (Journal) |
| Sprache: | Englisch |
| Veröffentlicht: |
2017
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| In: |
Rad Hrvatske Akademije Znanosti i Umjetnosti, Razred za Matematičke, Fizičke, Kemijske i Tehničke Znanosti
Year: 2017, Jahrgang: 21, Pages: 99-116 |
| DOI: | 10.21857/ydkx2c3rp9 |
| Online-Zugang: | Verlag, kostenfrei, Volltext: http://dx.doi.org/10.21857/ydkx2c3rp9 Verlag, kostenfrei, Volltext: https://hrcak.srce.hr/index.php?show=clanak&id_clanak_jezik=274961 
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| Verfasserangaben: | Anna Marciniak-Czochra and Andro Mikelić |
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| 520 | |a We study a shadow limit (the infinite diffusion coefficientlimit) 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. | ||
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