Solutions of Kirchhoff plate equations with internal damping and logarithmic nonlinearity

Date

2021-03-29

Authors

Pereira, Ducival C.
Cordeiro, Sebastiao
Raposo, Carlos Alberto
Maranhao, Celsa

Journal Title

Journal ISSN

Volume Title

Publisher

Texas State University, Department of Mathematics

Abstract

In this article we study the existence of weak solutions for the nonlinear initial boundary value problem of the Kirchhoff equation utt + Δ2u + M(∥∇u∥2) (-Δu) + ut = u ln |u|2, in Ω x (0, T), u(x, 0) = u0(x), ut(x, 0) = u1(x), x ∈ Ω, u(x, t) = ∂u/∂η (x, t) = 0, x ∈ ∂Ω, t ≥ 0, where Ω is a bounded domain in ℝ2 with smooth boundary ∂Ω, T > 0 is a fixed but arbitrary real number, M(s) is a continuous function on [0, +∞) and η is the unit outward normal on ∂Ω. Our results are obtained using the Galerkin method, compactness approach, potential well corresponding to the logarithmic nonlinearity, and the energy estimates due to Nakao.

Description

Keywords

Extensible beam, Existence of solutions, Asymptotic behavior, Logarithmic source term

Citation

Pereira, D., Cordeiro, S., Raposo, C., & Maranhão, C. (2021). Solutions of Kirchhoff plate equations with internal damping and logarithmic nonlinearity. <i>Electronic Journal of Differential Equations, 2021</i>(21), pp. 1-14.

Rights

Attribution 4.0 International

Rights Holder

Rights License