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 large time behavior of solutions are also discussed.
Funding Statement
N. Tsuge's research is partially supported by Grant-in-Aid for Scientific Research (C) 17K05315, Japan.
Acknowledgments
The authors would like to express their hearty gratitude to Professor Masaharu Nagayama for attracting them this problem, and for letting them know some results on (BZ). The authors would also like to express their thanks to Professor Shinya Miyajima for sending them various benefit comments.
Citation
S Kondo. NOVRIANTI. O Sawada. N Tsuge. "A well-posedness for the reaction diffusion equations of Belousov-Zhabotinsky reaction." Osaka J. Math. 58 (1) 59 - 70, January 2021.
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