Title

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 (C0) semigroup generated by the realizations of the operators Au = αu' ' + βu' or Au = b(au')' + βu' in C[0, 1] with general Wentzell boundary conditions of the type lim x→j Au(x)+eb(x)u'(x) = 0 for j = 0, 1 in C[0, 1]. Here the functions a, α, β, b,b̃ are assumed to be in C[0, 1], with a, α ε C1(0, 1), a(x) > 0, α(x) > 0, in (0, 1), b(x) > 0 in [0, 1] and a, or α, possibly degenerate at the endpoints, i.e. a, or α, allowed to vanish at 0 and 1. © SPM.

Publication Title

Boletim da Sociedade Paranaense de Matematica

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