Stability of the Steady States in Multidimensional Reaction Diffusion Systems Arising in Combustion Theory

Qingxia Li and Xinyao Yang ()
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Qingxia Li: Department of Mathematics and Computer Science, Fisk University, Nashville, TN 37208, USA
Xinyao Yang: Department of Applied Mathematics, Xi’an Jiaotong-Liverpool University, Suzhou 215123, China

Energies, 2022, vol. 15, issue 21, 1-22

Abstract: We prove that the steady states of a class of multidimensional reaction–diffusion systems are asymptotically stable at the intersection of unweighted space and exponentially weighted Sobolev spaces, paying particular attention to a special case, namely, systems of equations that arise in combustion theory. The steady-state solutions considered here are the end states of the planar fronts associated with these systems. The present work can be seen as a complement to the previous results on the stability of multidimensional planar fronts.

Keywords: planar front; steady state; nonlinear stability; exponential weights (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2022
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