Qualitative results for parabolic equations involving the p-Laplacian under dynamical boundary conditions - Archive ouverte HAL Access content directly
Journal Articles North-Western European Journal of Mathematics Year : 2018

Qualitative results for parabolic equations involving the p-Laplacian under dynamical boundary conditions

Abstract

We discuss comparison principles, the asymptotic behaviour, and the occurrence of blow up phenomena for nonlinear parabolic problems involving the p-Laplacian operator of the form    ∂ t u = ∆ p u + f (t, x, u) in Ω for t > 0, σ∂ t u + |∇u| p−2 ∂ ν u = 0 on ∂Ω for t > 0, u(0, •) = u 0 in Ω, where Ω is a bounded domain of R N with Lipschitz boundary, and where ∆ p u := div |∇u| p−2 ∇u is the p-Laplacian operator for p > 1. As for the dynamical time lateral boundary condition σ∂ t u + |∇u| p−2 ∂ ν u = 0 the coefficient σ is assumed to be a nonnegative constant. In particular, the asymptotic behaviour in the large for the parameter dependent nonlinearity f (•, •, u) = λ|u| q−2 u will be investigated by means of the evolution of associated norms.
Fichier principal
Vignette du fichier
becumaNWEJM ms. 16-48 revised version.pdf (335.92 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-03715299 , version 1 (06-07-2022)

Identifiers

  • HAL Id : hal-03715299 , version 1

Cite

Joachim von Below, Mabel Cuesta, Gaëlle Pincet Mailly. Qualitative results for parabolic equations involving the p-Laplacian under dynamical boundary conditions. North-Western European Journal of Mathematics, 2018, 4, pp.59-97. ⟨hal-03715299⟩
19 View
47 Download

Share

Gmail Facebook X LinkedIn More