Chapter 6 H∞ well-posedness for degenerate p-evolution models of higher order with time-dependent coefficients

Abstract

In this paper we deal with time dependent p-evolution Cauchy problems. The differential operators have characteristics of variable multiplicity. We consider a degeneracy only in t=0. We shall prove a well-posedness result in the scale of Sobolev spaces using a C 1-approach. In this way we will prove H ∞ well-posedness with an (at most) finite loss of regularity.