Well-posedness and attractors for a super-cubic weakly damped wave equation with H−1 source term

Liu, Cuncai; Meng, Fengjuan; Sun, Chunyou

doi:10.1016/j.jde.2017.08.047

Cited by 14 publications

(6 citation statements)

References 25 publications

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“…These findings led to the rapid development of the theory for weakly damped wave equation with supercubic growth. In particular, global attractors for Shatah-Struwe solutions for supercubic case with forcing in H −1 have been studied by Liu et al [29], and the exponential attractors were investigated by Meng and Liu in [32]. We also mention the work [10] of Carvalho, Cholewa, and Dłotko who proved an existence of the weak global attractor for a concept of solutions for supercubic but subquintic case.…”

Section: Introductionmentioning

confidence: 96%

Convergence of Non-autonomous Attractors for Subquintic Weakly Damped Wave Equation

Banaśkiewicz

Kalita

2021

Appl Math Optim

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We study the non-autonomous weakly damped wave equation with subquintic growth condition on the nonlinearity. Our main focus is the class of Shatah–Struwe solutions, which satisfy the Strichartz estimates and coincide with the class of solutions obtained by the Galerkin method. For this class we show the existence and smoothness of pullback, uniform, and cocycle attractors and the relations between them. We also prove that these non-autonomous attractors converge upper-semicontinuously to the global attractor for the limit autonomous problem if the time-dependent nonlinearity tends to a time independent function in an appropriate way.

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Section: Introductionmentioning

confidence: 96%

Convergence of Non-autonomous Attractors for Subquintic Weakly Damped Wave Equation

Banaśkiewicz

Kalita

2021

Appl Math Optim

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“…These findings led to the rapid development of the theory for weakly damped wave equation with supercubic growth. In particular, global attractors for Shatah-Struwe solutions for supercubic case with forcing in H −1 have been studied by Liu, Meng, and Sun [29], and the exponential attractors were investigated by Meng and Liu in [32]. We also mention the work [10] of Carvalho, Cholewa, and D lotko who obtained an existence of the weak global attractor for a concept of solutions for supercubic but subquintic case.…”

Section: Introductionmentioning

confidence: 98%

Convergence of non-autonomous attractors for subquintic weakly damped wave equation

Banaśkiewicz¹,

Kalita²

2021

Preprint

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We study the non-autonomous weakly damped wave equation with subquintic growth condition on the nonlinearity. Our main focus is the class of Shatah-Struwe solutions, which satisfy the Strichartz estimates and are coincide with the class of solutions obtained by the Galerkin method. For this class we show the existence and smoothness of pullback, uniform, and cocycle attractors and the relations between them. We also prove that these non-autonomous attractors converge upper-semicontinuously to the global attractor for the limit autonomous problem if the time-dependent nonlinearity tends to time independent function in an appropriate way.

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“…Working on the Shatah-Struwe solution semigroup arising from problem (1.1), Kalantarov et al [17] proved the existence and regularities of the compact global attractor in the case of sub-quintic and quintic growth rates of non-linearitiy f . Then, Liu et al [22,23,26] established the translational regular solution and studied the long-time behaviour of problem (1.1) with lower regular forcing (g ∈ H −1 ) and super-cubic non-linearity in both bounded and unbounded domains in R 3 . Recently, Savostianov and Zelik [31] studied the damped quintic wave equations with measure-driven and non-autonomous external forces in the 3-D perodic boundary conditions case.…”

Section: Introductionmentioning

confidence: 99%

Strong attractors for weakly damped quintic wave equation in bounded domains

Yan¹,

Tang²,

Zhong³

2022

Preprint

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In this paper, we study the longtime dynamics for the weakly damped wave equation with quintic nonlinearity in a bounded smooth domain of R 3 . Based on the Strichartz estimates for the case of bounded domains, we establish the existence of a strong global attractor in the phase space H 2 (Ω)∩H 1 0 (Ω)×H 1 0 (Ω). Moreover, the finite fractal dimension of the attractor is also shown with the help of the quasi-stable estimation.

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Well-posedness and attractors for a super-cubic weakly damped wave equation with H−1 source term

Cited by 14 publications

References 25 publications

Convergence of Non-autonomous Attractors for Subquintic Weakly Damped Wave Equation

Convergence of Non-autonomous Attractors for Subquintic Weakly Damped Wave Equation

Convergence of non-autonomous attractors for subquintic weakly damped wave equation

Strong attractors for weakly damped quintic wave equation in bounded domains

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