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ATTRACTORS FOR LATTICE DYNAMICAL SYSTEMS

PETER W. BATES

Department of Mathematics, Brigham Young University, Provo, Utah 84602, USA

Partially supported by NSF grants DMS 9970894 and 9974340.

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KENING LU

Department of Mathematics, Brigham Young University, Provo, Utah 84602, USA

Partially supported by NSF grant DMS 9970894.

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BIXIANG WANG

Department of Applied Mathematics, Tsinghua University, Beijing 100084, P.R. China

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https://doi.org/10.1142/S0218127401002031Cited by:205 (Source: Crossref)

Abstract

We study the asymptotic behavior of solutions for lattice dynamical systems. We first prove asymptotic compactness and then establish the existence of global attractors. The upper semicontinuity of the global attractor is also obtained when the lattice differential equations are approached by finite-dimensional systems.