Nonlinear perturbations of the Kirchhoff equation
Date
2017-03-21
Authors
Miranda, Manuel M.
Louredo, Aldo T.
Medeiros, Luiz A.
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
In this article we study the existence and uniqueness of local solutions for the initial-boundary value problem for the Kirchhoff equation
u″ - M(t, ∥u(t)∥2)∆u + |u|ρ = ƒ in Ω x (0, T0),
u = 0 on Γ0 x]0, T0[,
∂u/∂v + δh(u′) = 0 on Γ1 x]0, T0[,
where Ω is a bounded domain of ℝn with its boundary consisting of two disjoint parts Γ0 and Γ1; ρ > 1 is a real number; v(x) is the exterior unit normal vector at x ∈ Γ1 and δ(x), h(s) are real functions defined in Γ1 and ℝ, respectively. Our result is obtained using the Galerkin method with a special basis, the Tartar argument, the compactness approach, and a Fixed-Point method.
Description
Keywords
Kirchhoff equation, Nonlinear boundary condition, Existence of solutions
Citation
Miranda, M. M., Louredo, A. T., & Medeiros, L. A. (2017). Nonlinear perturbations of the Kirchhoff equation. <i>Electronic Journal of Differential Equations, 2017</i>(77), pp. 1-21.
Rights
Attribution 4.0 International