On some classes of differential operators generating analytic semigroups (Q2708556)

The authors give a systematic study of the analyticity of the \(C_0\)-semigroups generated by NEWLINE\[NEWLINEAu:= \alpha u''+\beta u'NEWLINE\]NEWLINE with the so-called Wentzell domain \(D(V)= \{u\in C[0,1]\cap C^2(0,1):\lim_{x\to j} Au(x)= 0\) for \(j= 0,1\}\), or Timmermans domain \(D(T):= \{u\in C[0,1]\cap C^2(0,1): \lim_{x\to j} Au(x)\in \mathbb{R}\) for \(j= 0,1\}\), or else \(D(N):= \{u\in C[0,1]\cap C^2(0,1): \alpha u'\in C^1[0,1]\), \(\lim_{x\to 0,1} \alpha(x) u'(x)= 0\}\).NEWLINENEWLINENEWLINEUnder different verifiable conditions on the functions \(\alpha\), \(\beta\), the authors prove that \((A,D(V))= (A,D(T))\) and it generates an analytic semigroup on \(C[0,1]\) (and in some cases, \(D(V)= D(T)= D(N)\)).NEWLINENEWLINEFor the entire collection see [Zbl 0957.00037].