In this paper, we study a viscoelastic wave equations of the Kirchhoff type u′′ −f (x) ( M(k?xuk22 )Dxu− Z t 0 g(t −s)Dxu(s)ds ) = auln |u|k (1) defined in any spaces dimension. It is well known that from a class of nonlinearities the logarithmic nonlinearity is distinguished by several interesting physical properties. We use weighted spaces to establish the long-time behavior of solution of (1). Furthermore, under convenient hypotheses on g and the initial data, the local-in-time existence of solution is established.
Digital Object Identifier (DOI)
Zennir, Khaled; Boulaaras, Salah; Haiour, Mohamed; and Bayoud, Mohsin
"Wave Equation with Logarithmic Nonlinearities in Kirchhoff Type,"
Applied Mathematics & Information Sciences: Vol. 10
, Article 18.
Available at: https://dc.naturalspublishing.com/amis/vol10/iss6/18