Close-to-equilibrium regularity for reaction-diffusion systems

2017/04/05 by Tang, Bao Quoc
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1704.01287

Abstract

The close-to-equilibrium regularity of solutions to a class of reaction-diffusion systems is investigated. The considered systems typically arise from chemical reaction networks and satisfy a complex balanced condition. Under some restrictions on spatial dimensions (d≤ 4) and order of nonlinearities (μ= 1 + 4/d), we show that if the initial data is close to a complex balanced equilibrium in L²-norm, then classical solutions are shown global and converging exponentially to equilibrium in L^∞-norm. Possible extensions to higher dimensions and order of nonlinearities are also discussed. The results of this paper improve the recent work [M.J. Cáceres and J.A. Cañizo, Nonlinear Analysis: TMA 159 (2017): 62-84].

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