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Volume 40, Issue 4
Existence of Global Attractor for Weakly Damped FDS Nonlinear Wave Equations

Boling Guo & Ying Zhang

DOI: 10.4208/aam.OA-2024-0009

Ann. Appl. Math., 40 (2024), pp. 333-346.

Published online: 2025-01

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  • Abstract

The paper investigates the well-posedness of global solutions and the existence of global attractors for weakly damped FDS nonlinear wave equations. It establishes the well-posedness of weak solutions using Galerkin approximation and a priori estimate. Subsequently, a dynamical system is constructed based on the well-posedness of the solution. The existence of a bounded absorbing set for the equations and the smooth properties of the operator semigroup are presented, leading to the existence of a global attractor.

  • Keywords

Global attractors, a priori estimate, FDS nonlinear wave equations.

  • AMS Subject Headings

35B40, 35B41, 35B45

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAM-40-333, author = {Guo , Boling and Zhang , Ying}, title = {Existence of Global Attractor for Weakly Damped FDS Nonlinear Wave Equations}, journal = {Annals of Applied Mathematics}, year = {2025}, volume = {40}, number = {4}, pages = {333--346}, abstract = {

The paper investigates the well-posedness of global solutions and the existence of global attractors for weakly damped FDS nonlinear wave equations. It establishes the well-posedness of weak solutions using Galerkin approximation and a priori estimate. Subsequently, a dynamical system is constructed based on the well-posedness of the solution. The existence of a bounded absorbing set for the equations and the smooth properties of the operator semigroup are presented, leading to the existence of a global attractor.

}, issn = {}, doi = {https://doi.org/10.4208/aam.OA-2024-0009}, url = {http://global-sci.org/intro/article_detail/aam/23775.html} }
TY - JOUR T1 - Existence of Global Attractor for Weakly Damped FDS Nonlinear Wave Equations AU - Guo , Boling AU - Zhang , Ying JO - Annals of Applied Mathematics VL - 4 SP - 333 EP - 346 PY - 2025 DA - 2025/01 SN - 40 DO - http://doi.org/10.4208/aam.OA-2024-0009 UR - https://global-sci.org/intro/article_detail/aam/23775.html KW - Global attractors, a priori estimate, FDS nonlinear wave equations. AB -

The paper investigates the well-posedness of global solutions and the existence of global attractors for weakly damped FDS nonlinear wave equations. It establishes the well-posedness of weak solutions using Galerkin approximation and a priori estimate. Subsequently, a dynamical system is constructed based on the well-posedness of the solution. The existence of a bounded absorbing set for the equations and the smooth properties of the operator semigroup are presented, leading to the existence of a global attractor.

Guo , Boling and Zhang , Ying. (2025). Existence of Global Attractor for Weakly Damped FDS Nonlinear Wave Equations. Annals of Applied Mathematics. 40 (4). 333-346. doi:10.4208/aam.OA-2024-0009
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