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.
@article{7525,
title = {General Wentzell boundary conditions, differential operators and analytic semigroups in C[0, 1] - doi: 10.5269/bspm.v20i1-2.7525},
journal = {Boletim da Sociedade Paranaense de Matem\'atica},
volume = {23},
year = {2009},
doi = {10.5269/bspm.v20i1-2.7525},
language = {EN},
url = {http://dml.mathdoc.fr/item/7525}
}
Favini, Angelo; Goldstein, Jerome A.; Goldstein, Gisèle R.; Romanelli, Silvia. General Wentzell boundary conditions, differential operators and analytic semigroups in C[0, 1] - doi: 10.5269/bspm.v20i1-2.7525. Boletim da Sociedade Paranaense de Matemática, Tome 23 (2009) . doi : 10.5269/bspm.v20i1-2.7525. http://gdmltest.u-ga.fr/item/7525/