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On the wave equation with hyperbolic dynamical boundary conditions, interior and boundary damping and supercritical sources.
- Source :
-
Journal of Differential Equations . Nov2018, Vol. 265 Issue 10, p4873-4941. 69p. - Publication Year :
- 2018
-
Abstract
- The aim of this paper is to study the problem { u t t − Δ u + P ( x , u t ) = f ( x , u ) in ( 0 , ∞ ) × Ω , u = 0 on ( 0 , ∞ ) × Γ 0 , u t t + ∂ ν u − Δ Γ u + Q ( x , u t ) = g ( x , u ) on ( 0 , ∞ ) × Γ 1 , u ( 0 , x ) = u 0 ( x ) , u t ( 0 , x ) = u 1 ( x ) in Ω ‾ , where Ω is a bounded open subset of R N with C 1 boundary ( N ≥ 2 ), Γ = ∂ Ω , Γ 1 is relatively open on Γ, Δ Γ denotes the Laplace–Beltrami operator on Γ, ν is the outward normal to Ω, and the terms P and Q represent nonlinear damping terms, while f and g are nonlinear perturbations. In the paper we establish local and global existence, uniqueness and Hadamard well-posedness results when source terms can be supercritical or super-supercritical. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00220396
- Volume :
- 265
- Issue :
- 10
- Database :
- Academic Search Index
- Journal :
- Journal of Differential Equations
- Publication Type :
- Academic Journal
- Accession number :
- 131494980
- Full Text :
- https://doi.org/10.1016/j.jde.2018.06.022