The non-autonomous wave equation with general Wentzell boundary conditions
We study the problem of the well-posedness for the abstract Cauchy problem associated to the non-autonomous one-dimensional wave equation utt = A(t)u with general Wentzell boundary conditions A(t)u(j, t) + (-1) j+1βj(t)∂u/∂x)(j, t) + γ j(t)u(j, t) = 0, for j = 0, 1. Here A(t)u := (a(x, t)u x)x, a(x, t) ≥ ε > 0 in [0, 1] × [0,+∞) and βj(t) > 0, γj(t) ≥ 0, (γ0(t), γ1(t)) ≠ (0, 0). Under suitable regularity conditions on α, βj, γj we prove the well-posedness in a suitable (energy) Hilbert space. © 2005 The Royal Society of Edinburgh.
Royal Society of Edinburgh - Proceedings A
Favini, A., Gal, C., Goldstein, G., Goldstein, J., & Romanelli, S. (2005). The non-autonomous wave equation with general Wentzell boundary conditions. Royal Society of Edinburgh - Proceedings A, 135 (2), 317-329. https://doi.org/10.1017/s0308210500003905