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 .
Highlights
Main ResultsLet us start by considering an operator of the type Au := αu where the coefficient α may degenerate at the boundary, but with degeneracy of low order
It is worthwhile to point out that the recent results by Xiao and Liang [21] and Batkai and Engel [2] revealed that, thanks to a suitable abstract framework, analyticity with general Wentzell boundary condition for second order equations in C[0, 1] can be obtained as a byproduct of the study of cosine families with general Wentzell boundary conditions
Let us start by considering an operator of the type Au := αu where the coefficient α may degenerate at the boundary, but with degeneracy of low order
Summary
Let us start by considering an operator of the type Au := αu where the coefficient α may degenerate at the boundary, but with degeneracy of low order.
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