An application of semigroups of locally Lipschitz operators to Carrier equations with acoustic boundary conditions

A generation theorem of semigroups of locally Lipschitz operators on a subset of a real Banach space is given and applied to the problem of the well-posedness of the Carrier equation utt −κ( u 2) u+γ |ut |p−1ut = 0 in Ω ×(0,∞) with acoustic boundary condition, where p >2 and Ω is a bounded domain in an arbitrary dimensional space. © 2007 Elsevier Inc. All rights reserved.