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<p>We study the measure dynamics of non-autonomous stochastic sine-Gordon lattice equations driven by nonlinear noise. Based on the Feller property, we prove that the dual operators of transition operators generate a continuous measure process. Based on the exponential decay of moments, we use a two-stage method to prove the pullback absorption and pullback asymptotic tightness, which allows us to construct a pullback measure attractor for the dual measure process. Furthermore, the pullback measure attractor is approximated by the finite-dimensionally truncated measure attractor under the Hausdorff semimetric between measure sets.</p>

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Finite-Dimensional Approximation of Pullback Measures Attractors for Nonlinearly Stochastic Sine-Gordon Equations on Infinite Lattice

  • 期刊论文

  • 发表日期：

    2026年7月22日

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  • Shuya Chen,
  • Yangrong Li

摘要

We study the measure dynamics of non-autonomous stochastic sine-Gordon lattice equations driven by nonlinear noise. Based on the Feller property, we prove that the dual operators of transition operators generate a continuous measure process. Based on the exponential decay of moments, we use a two-stage method to prove the pullback absorption and pullback asymptotic tightness, which allows us to construct a pullback measure attractor for the dual measure process. Furthermore, the pullback measure attractor is approximated by the finite-dimensionally truncated measure attractor under the Hausdorff semimetric between measure sets.