Well-posedness and asymptotic stability results for a viscoelastic plate equation with a logarithmic nonlinearity. Issue 1 (2nd January 2020)

• Record Type: Journal Article
• Authors: Al-Gharabli, Mohammad M.; Guesmia, Aissa; Messaoudi, Salim A.
• Is Part Of: Applicable analysis. Volume 99:Issue 1(2020)
• Page Start: 50
• Page End: 74
• Publication Date: 2020-01-02
• Subjects: Asymptotic stability -- viscoelastic -- plate equation -- logarithmic nonlinearity; 35B35 -- 35L55 -- 75D05 -- 74D10 -- 93D20; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2018.1484910
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: In this paper, we consider a viscoelastic plate equation with a velocity-dependent material density and a logarithmic nonlinearity. Using the Faedo-Galaerkin approximations and the multiplier method, we establish the existence of the solutions of the problem and we prove an explicit and general decay rate result. These results extend and improve many results in the literature.