Title

The non-autonomous wave equation with general Wentzell boundary conditions

Abstract

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.

Publication Title

Royal Society of Edinburgh - Proceedings A

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