Discontinuous stationary solutions to certain reaction-diffusion systems

Szymon Cygan (), Anna Marciniak-Czochra () and Grzegorz Karch ()
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Szymon Cygan: Uniwersytet Wrocławski
Anna Marciniak-Czochra: University of Heidelberg
Grzegorz Karch: Uniwersytet Wrocławski

Partial Differential Equations and Applications, 2022, vol. 3, issue 4, 1-15

Abstract: Abstract Systems consisting of a single ordinary differential equation coupled with one reaction-diffusion equation in a bounded domain and with the Neumann boundary conditions are studied in the case of particular nonlinearities from the Brusselator model, the Gray-Scott model, the Oregonator model and a certain predator-prey model. It is shown that the considered systems have the both smooth and discontinuous stationary solutions, however, only discontinuous ones can be stable.

Keywords: Reaction-diffusion equations; Stationary solutions; stable and unstable stationary solutions; 35K57; 35B35; 35B36; 92C15 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s42985-022-00188-x

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