Stability estimates for nonlinear hyperbolic problems with nonlinear Wentzell boundary conditions
Abstract
Of concern is the nonlinear hyperbolic problem with nonlinear dynamic boundary conditions, for t ≥ 0 x ∈ Ω ⊂ ℝN; the last equation holds on the boundary ∂Ω. Here A = {aij(x)}ij is a real, hermitian, uniformly positive definite N × N matrix; β ∈ C (∂Ω), with β ≥ 0; γ: Ω × ℝ → ℝ; δ ∂Ω × ℝ → ℝ; c ∂Ω → ℝ; q ≥ 0, ΔLB is the Laplace-Beltrami operator on ∂Ω and ∂vAu is the conormal derivative of u with respect to A; everything is sufficiently regular. We prove explicit stability estimates of the solution u with respect to the coefficients A, β γ δ, c, q and the initial conditions f, g. Our arguments cover the singular case of a problem with q = 0 which is approximated by problems with positive q. © 2012 Springer Basel AG.
Publication Title
Zeitschrift fur Angewandte Mathematik und Physik
Recommended Citation
Coclite, G., Goldstein, G., & Goldstein, J. (2013). Stability estimates for nonlinear hyperbolic problems with nonlinear Wentzell boundary conditions. Zeitschrift fur Angewandte Mathematik und Physik, 64 (3), 733-753. https://doi.org/10.1007/s00033-012-0261-5
