Aufsatz(elektronisch)#11. Dezember 2022
Global existence and stability of solution for a p-Kirchhoff type hyperbolic equation with damping and source terms
In: Studia Universitatis Babeş-Bolyai. Mathematica, Band 67, Heft 4, S. 817-827
"; Ouaoua, Amar; Khaldi, Aya; Maouni, Messaoud; Laboratory of Applied Mathematics and History and Didactics of Mathematics, Faculty of Sciences, University of 20 August 1955, Skikda, Algeria e-mail: a.ouaoua@univ-skikda.dz & ouaouaama21@gmail.com"; "Laboratory of Applied Mathematics and History and Didactics of Mathematics, Faculty of Sciences, University of 20 August 1955, Skikda, Algeria e-mail: ayakhaldi21@gmail.com"; "Laboratory of Applied Mathematics and History and Didactics of Mathematics, Faculty of Sciences, University of 20 August 1955, Skikda, Algeria e-mail: m.maouni@univ-skikda.dz & maouni21@gmail.com"
"; Ouaoua, Amar; Khaldi, Aya; Maouni, Messaoud; Laboratory of Applied Mathematics and History and Didactics of Mathematics, Faculty of Sciences, University of 20 August 1955, Skikda, Algeria e-mail: a.ouaoua@univ-skikda.dz & ouaouaama21@gmail.com"; "Laboratory of Applied Mathematics and History and Didactics of Mathematics, Faculty of Sciences, University of 20 August 1955, Skikda, Algeria e-mail: ayakhaldi21@gmail.com"; "Laboratory of Applied Mathematics and History and Didactics of Mathematics, Faculty of Sciences, University of 20 August 1955, Skikda, Algeria e-mail: m.maouni@univ-skikda.dz & maouni21@gmail.com"
ISSN: 2065-961X
"In this paper, we consider a nonlinear $p-$Kirchhoff type hyperbolic equation with damping and source terms $$u_{tt}-M\left( \underset{\Omega }{\int }\left\vert \nabla u\right\vert ^{p}dx\right) \Delta _{p}u+\left\vert u_{t}\right\vert ^{m-2}u_{t}=\left\vert u\right\vert ^{r-2}u.$$ Under suitable assumptions and positive initial energy, we prove the global existence of solution by using the potential energy and Nehari's functionals. Finally, the stability of equation is established based on Komornik's integral inequality."