Benjamin-Bona-Mahony 方程在三维通道中的全局吸引子存在性

Abstract

Abstract:

This article establishes the existence of global attractors for the (generalized) Benjamin-Bona-Mahony equation in a three-dimensional channel, when the nonlinear term satisfies the growth condition of order $m=2$, which extends the result obtained by Wang-Fussner-Bi [Wang B, Fussner D W, Bi C. J Phys A, 2007, 40(34): 10491-10504]. In particular, in order to prove the asymptotic compactness of the solution semigroup, we prove firstly the weak continuity property, and secondly the convergence in norm by taking advantage of the energy equation method.

Key words: Benjamin-Bona-Mahony equation, global attractor, asymptotic compactness, weak continuity.

CLC Number:

O175.29

Ling Wan, Yuying Xu, Tengfei Zhang. Existence of Global Attractors of the Benjamin-Bona-Mahony Equation in Three-Dimensional Channel[J].Acta mathematica scientia,Series A, 2026, 46(3): 1015-1024.

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References 35

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Existence of Global Attractors of the Benjamin-Bona-Mahony Equation in Three-Dimensional Channel

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