Global existence and exponential decay for a viscoelastic equation with not necessarily decreasing kernel

• Autorzy: Alaeddine Draifia

Identyfikatory

DOI

10.1515/jaa-2021-2075

• Języki publikacji: EN

Abstrakty

EN

In this paper, we consider the nonlinear viscoelastic equation u_tt − Δu + ^t∫₀h(t − s)Δu(s) ds + a(x)|ut|^mut + |u|^γu = 0 in a bounded domain with kernels not necessarily exponentially decaying to zero and we obtain an asymptotic stability result of global solutions.

Słowa kluczowe

EN

general decay; exponential decay; nonlinear localized damping

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2022
• Tom: Vol. 28, nr 2
• Strony: 219--236
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Alaeddine Draifia

• Department of Mathematics and Informatics, Institute of Sciences, University Center Aflou, Laghouat; and Laboratory of Mathematics, Informatics and Systems (LAMIS), Larbi Tebessi University, 12002 Tebessa, Algeria

• https://orcid.org/0000-0001-9565-6982

Bibliografia

• [1] S. Berrimi and S. A. Messaoudi, Exponential decay of solutions to a viscoelastic equation with nonlinear localized damping, Electron. J. Differential Equations 2004 (2004), Paper No. 88.
• [2] N. Boumaza and S. Boulaaras, General decay for Kirchhoff type in viscoelasticity with not necessarily decreasing kernel, Math. Methods Appl. Sci. 41 (2018), no. 16, 6050-6069.
• [3] M. M. Cavalcanti, V. N. Domingos Cavalcanti and P. Martinez, General decay rate estimates for viscoelastic dissipative systems, Nonlinear Anal. 68 (2008), no. 1, 177-193.
• [4] M. M. Cavalcanti, V. N. Domingos Cavalcanti, J. S. Prates Filho and J. A. Soriano, Existence and uniform decay rates for viscoelastic problems with nonlinear boundary damping, Differential Integral Equations 14 (2001), no. 1, 85-116.
• [5] M. M. Cavalcanti, V. N. Domingos Cavalcanti and J. A. Soriano, Exponential decay for the solution of semilinear viscoelastic wave equations with localized damping, Electron. J. Differential Equations 2002 (2002), Paper No. 44.
• [6] M. M. Cavalcanti and H. P. Oquendo, Frictional versus viscoelastic damping in a semilinear wave equation, SIAM J. Control Optim. 42 (2003), no. 4, 1310-1324.
• [7] W. Liu, Exponential or polynomial decay of solutions to a viscoelastic equation with nonlinear localized damping, J. Appl. Math. Comput. 32 (2010), no. 1, 59-68.
• [8] M. Medjden and N.-E. Tatar, Asymptotic behavior for a viscoelastic problem with not necessarily decreasing kernel, Appl. Math. Comput. 167 (2005), no. 2, 1221-1235.
• [9] F. Mesloub and S. Boulaaras, General decay for a viscoelastic problem with not necessarily decreasing kernel, J. Appl. Math. Comput. 58 (2018), no. 1-2, 647-665.
• [10] A. Zarai, A. Draifia and S. Boulaaras, Blow-up of solutions for a system of nonlocal singular viscoelastic equations, Appl. Anal. 97 (2018), no. 13, 2231-2245.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2024).