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

• Verfasst von: Marciniak-Czochra, Anna [VerfasserIn]
• Verfasst von: Mikelić, Andro [VerfasserIn]
• Titel: Shadow limit for parabolic-ODE systems through a cut-off argument
• Verf.angabe: Anna Marciniak-Czochra and Andro Mikelić
• Fussnoten: Gesehen am 28.06.2018
• Titel Quelle: Enthalten in: Hrvatska Akademija Znanosti i Umjetnosti. Razred za Matematičke, Fizičke, Kemijske i Tehničke Znanosti: Rad Hrvatske Akademije Znanosti i Umjetnosti, Razred za Matematičke, Fizičke, Kemijske i Tehničke Znanosti / Matematičke Znanosti
• Jahr Quelle: 2017
• Band/Heft Quelle: Vol. 21=532(2017), 18 Seiten
• DOI: doi:10.21857/ydkx2c3rp9
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1577011074

Abstract

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.