INVARIANT MANIFOLDS FOR THE NONAUTONOMOUS BOISSONADE SYSTEM IN THREE-DIMENSIONAL TORUS

Na Liu

doi:10.11948/20210321

2021 Volume 11 Issue 6

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Na Liu. INVARIANT MANIFOLDS FOR THE NONAUTONOMOUS BOISSONADE SYSTEM IN THREE-DIMENSIONAL TORUS[J]. Journal of Applied Analysis & Computation, 2021, 11(6): 3133-3156. doi: 10.11948/20210321

Citation:

Na Liu. INVARIANT MANIFOLDS FOR THE NONAUTONOMOUS BOISSONADE SYSTEM IN THREE-DIMENSIONAL TORUS[J]. Journal of Applied Analysis & Computation, 2021, 11(6): 3133-3156. doi: 10.11948/20210321

INVARIANT MANIFOLDS FOR THE NONAUTONOMOUS BOISSONADE SYSTEM IN THREE-DIMENSIONAL TORUS

Na Liu

Department of Mathematics, Shanghai Normal University, Guilin Road, 200234 Shanghai, China

Author Bio: Email address: naliumath@126.com (N. Liu)

Abstract

Abstract

We undertake a study of invariant manifolds for the nonautonomous Boissonade system in three-dimensional torus. The system, exhibiting Turing structures, is a activator-inhibitor model for describing the relation between the genuine homogeneous 2D systems and the 3D monolayers. Assuming the diffusivity of the activator be sufficiently large, we prove the existence of a finite-dimensional Lipschitz manifold. The manifold is locally forward invariant and pullback attracts exponentially only those solutions with initial values having a certain regularity. If more assumptions on the external forces are made such that the symbol space is compact, we prove that the manifold is of global type.
- Boissonade system /
- three-dimensional torus /
- nonautonomous dynamical system /
- finite-dimensional manifold of global type
MSC: 35B42, 37B55, 37D10

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References

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