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