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<p>This paper investigates an abstract Kirchhoff-type suspension bridge model with fractional internal damping. Using the theory of semigroups of bounded linear operators, we establish the existence and uniqueness of global strong solutions for the model. Through the theory of continuous (nonlinear) operator semigroups, we prove that the associated semigroup is gradient and asymptotically compact, which enables us to demonstrate the existence of a global attractor characterized by the system’s stationary solutions. Furthermore, we show that the semigroup is asymptotically quasistable, yielding two important consequences: (1) The attractor has finite fractal dimension and (2) enhanced solution regularity.</p>

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Existence of global solution and global attractor for a suspended bridge system of Kirchhoff type with fractional derivative damping

  • 期刊论文

  • 发表日期：

    2026年1月19日

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  • Rafael O. de Jesus,
  • Mirelson M. Freitas,
  • Carlos A. Raposo,
  • Carlos A. Nonato

摘要

This paper investigates an abstract Kirchhoff-type suspension bridge model with fractional internal damping. Using the theory of semigroups of bounded linear operators, we establish the existence and uniqueness of global strong solutions for the model. Through the theory of continuous (nonlinear) operator semigroups, we prove that the associated semigroup is gradient and asymptotically compact, which enables us to demonstrate the existence of a global attractor characterized by the system’s stationary solutions. Furthermore, we show that the semigroup is asymptotically quasistable, yielding two important consequences: (1) The attractor has finite fractal dimension and (2) enhanced solution regularity.