General Wentzell boundary conditions, differential operators and analytic semigroups in C[0, 1]

Abstract

We are concerned with the study of the analyticity of the (C_0)semigroup generated by the realizations of the operators Au = alpha 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, b, tilde{b} are assumed to be in C[0, 1], with a, alpha 2 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 , allowed to vanish at 0 and 1.

Keywords

• differential operators
• analytic semigroups
• Wentzell boundary conditions.