Stabilization of the wave equation with a nonlinear delay term in the boundary conditions

• Autorzy: Ghecham Wassila , Rebiai Salah-Eddine , Sidiali Fatima Zohra

Identyfikatory

DOI

10.1515/jaa-2021-2051

• Języki publikacji: EN

Abstrakty

EN

A wave equation in a bounded and smooth domain of ℝⁿ with a delay term in the nonlinear boundary feedback is considered. Under suitable assumptions, global existence and uniform decay rates for the solutions are established. The proof of existence of solutions relies on a construction of suitable approximating problems for which the existence of the unique solution will be established using nonlinear semigroup theory and then passage to the limit gives the existence of solutions to the original problem. The uniform decay rates for the solutions are obtained by proving certain integral inequalities for the energy function and by establishing a comparison theorem which relates the asymptotic behavior of the energy and of the solutions to an appropriate dissipative ordinary differential equation.

Słowa kluczowe

EN

wave equation; time delays; nonlinear boundary feedback; stabilization; decay rate

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2022
• Tom: Vol. 28, nr 1
• Strony: 35--55
• Opis fizyczny: Bibliogr. 24 poz.

Twórcy

autor

Ghecham Wassila

• LTM, University of Batna 2, Batna 05078, Algeria

autor

Rebiai Salah-Eddine

• LTM, University of Batna 2, Batna 05078, Algeria

• https://orcid.org/0000-0002-0595-0094

autor

Sidiali Fatima Zohra

• LTM, University of Batna 2, Batna 05078, Algeria,

Bibliografia

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Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).