A well-posedness for the reaction diffusion equations of Belousov-Zhabotinsky reaction

2019/03/26 by Shun Kondo, Novrianti Novrianti, Kondo, S. +8
Computer Science · Mathematics · Medicine · #Nonlinear Dynamics and Pattern Formation #Mathematical Biology Tumor Growth #Mathematical and Theoretical Epidemiology and Ecology Models

paper · pdf · doi:10.48550/arxiv.1903.10715

Abstract

The time-global existence of unique smooth positive solutions to the reaction diffusion equations of the Keener-Tyson model for the Belousov-Zhabotinsky reaction in the whole space is established with bounded non-negative initial data. Deriving estimates of semigroups and time evolution operators, and applying the maximum principle, the unique existence and the positivity of solutions are ensured by construction of time-local solutions from certain successive approximation. Invariant regions and long time behavior of solutions are also discussed.

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