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PreprintarXiv licencearXiv

Existence of pullback 𝒟-attractors for Kirchhoff wave equations with strong damping and delay

  • Bin Yang
  • Yuming Qin
  • Alain Miranville
  • Xuxiao Hou
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Abstract

This paper studies the existence of pullback 𝒟-attractors for non-autonomous Kirchhoff wave equations with strong damping and delay effects in the phase space ℰ = CH10(Ω) × CL2(Ω). The model contains a strong damping term −Δ∂t u, a nonlocal Kirchhoff term Ψ(|∇ u|2), a state-dependent delay term ϕ(t, ut), and a time-dependent external force $h(x, t)$. There appear to be no results on the pullback attractors of Kirchhoff wave equations involving both strong damping and delay effects in the literature. To this end, we establish delicate uniform estimates and employ the contraction function method to prove the pullback asymptotic compactness of the associated process, which yields the existence of pullback 𝒟-attractors.

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Cite

BibTeXRIS
BibTeX
@misc{yang2026existence,
  title = {{Existence of pullback \(\mathcalD\)-attractors for Kirchhoff wave equations with strong damping and delay}},
  author = {Bin Yang and Yuming Qin and Alain Miranville and Xuxiao Hou},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.15069},
  eprint = {2609.15069},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.15069},
}
RIS
TY  - UNPB
TI  - Existence of pullback 𝒟-attractors for Kirchhoff wave equations with strong damping and delay
AU  - Bin Yang
AU  - Yuming Qin
AU  - Alain Miranville
AU  - Xuxiao Hou
PY  - 2026
DA  - 2026/09/14
PB  - arXiv
DO  - 10.48550/arxiv.2609.15069
UR  - https://arxiv.org/abs/2609.15069
AB  - This paper studies the existence of pullback 𝒟-attractors for non-autonomous Kirchhoff wave equations with strong damping and delay effects in the phase space ℰ = C_H^1_0(Ω) × C_L^2(Ω). The model contains a strong damping term −Δ∂_t u, a nonlocal Kirchhoff term Ψ(|∇ u|^2), a state-dependent delay term ϕ(t, u_t), and a time-dependent external force $h(x, t)$. There appear to be no results on the pullback attractors of Kirchhoff wave equations involving both strong damping and delay effects in the literature. To this end, we establish delicate uniform estimates and employ the contraction function method to prove the pullback asymptotic compactness of the associated process, which yields the existence of pullback 𝒟-attractors.
ER  -