General Wentzell boundary conditions, differential operators and analytic semigroups in C[0, 1]
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}(...
Main Authors: | , , , |
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Format: | Article |
Language: | English |
Published: |
Sociedade Brasileira de Matemática
2002-11-01
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Series: | Boletim da Sociedade Paranaense de Matemática |
Subjects: | |
Online Access: | http://www.periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/7525/4341 |
Summary: | 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. |
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ISSN: | 0037-8712 2175-1188 |