Decay rate of the solutions to the Cauchy problem of the Lord Shulman thermoelastic Timoshenko model with distributed delay

• Autorzy: Choucha Abdelbaki , Boulaaras Salah , Jan Rashid , Alnegga Mohammad

Identyfikatory

DOI

10.1515/dema-2023-0143

• Języki publikacji: EN

Abstrakty

EN

In this study, we address a Cauchy problem within the context of the one-dimensional Timoshenko system, incorporating a distributed delay term. The heat conduction aspect is described by the Lord-Shulman theory. Our demonstration establishes that the dissipation resulting from the coupling of the Timoshenko system with Lord-Shulman’s heat conduction is sufficiently robust to stabilize the system, albeit with a gradual decay rate. To support our findings, we convert the system into a first-order form and, utilizing the energy method in Fourier space, and derive point wise estimates for the Fourier transform of the solution. These estimates, in turn, provide evidence for the slow decay of the solution.

Słowa kluczowe

EN

partial differential equation; decay rate; Lord-Shulman; thermoelasticity; mathematical operators; Fourier transform; distributed delay

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2024
• Tom: Vol. 57, nr 1
• Strony: art. no. 20230143
• Opis fizyczny: Bibliogr. 24 poz.

Twórcy

autor

Choucha Abdelbaki

• Department of Material Sciences, Faculty of Sciences, Amar Teleji Laghouat University, Laghouat, Algeria

autor

Boulaaras Salah

• Department of Mathematics, College of Science, Qassim University, Buraydah, 51452, Saudi Arabia

autor

Jan Rashid

• Institute of Energy Infrastructure (IEI), Department of Civil Engineering, College of Engineering, Universiti Tenaga Nasional (UNITEN), Putrajaya Campus, Jalan IKRAM-UNITEN, 43000 Kajang, Selangor, Malaysia

autor

Alnegga Mohammad

• Department of Mathematics, College of Science, Qassim University, Buraydah, 51452, Saudi Arabia

Bibliografia

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025).