General Wentzell boundary conditions, differential operators and analytic semigroups in C[0, 1] - doi: 10.5269/bspm.v20i1-2.7525

Abstract

We are concerned with the study of the analyticity of the (C_0) semigroup generated by the realizations of the operators Au = u'' + \beta u' or Au = b(au')' + \beta u' in C[0, 1] with general Wentzell boundary conditions of the type lim_{x \rightarrow j} Au(x)+\tilde b(x)u'(x) = 0 for j = 0, 1 in C[0, 1]. Here the functions a, \alpha , \beta , b, e \tilde b are assumed to be in C[0, 1], with a, \alpha \in C^1(0, 1), a(x) > 0,  \alpha(x) > 0, in (0, 1), b(x) > 0 in [0, 1] and a, or \alpha, possibly degenerate at the endpoints, i.e. a, or  \alpha allowed to vanish at 0 and 1.