Analyticity for some degenerate one-dimensional evolution equations

G. Metafune

Studia Mathematica (1998)

  • Volume: 127, Issue: 3, page 251-276
  • ISSN: 0039-3223

Abstract

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We study the analyticity of the semigroups generated by some degenerate second order differential operators in the space C([α,β]), where [α,β] is a bounded real interval. The asymptotic behaviour and regularity with respect to the space variable are also investigated.

How to cite

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Metafune, G.. "Analyticity for some degenerate one-dimensional evolution equations." Studia Mathematica 127.3 (1998): 251-276. <http://eudml.org/doc/216471>.

@article{Metafune1998,
abstract = {We study the analyticity of the semigroups generated by some degenerate second order differential operators in the space C([α,β]), where [α,β] is a bounded real interval. The asymptotic behaviour and regularity with respect to the space variable are also investigated.},
author = {Metafune, G.},
journal = {Studia Mathematica},
keywords = {analytic semigroups; Ventcel's boundary conditions},
language = {eng},
number = {3},
pages = {251-276},
title = {Analyticity for some degenerate one-dimensional evolution equations},
url = {http://eudml.org/doc/216471},
volume = {127},
year = {1998},
}

TY - JOUR
AU - Metafune, G.
TI - Analyticity for some degenerate one-dimensional evolution equations
JO - Studia Mathematica
PY - 1998
VL - 127
IS - 3
SP - 251
EP - 276
AB - We study the analyticity of the semigroups generated by some degenerate second order differential operators in the space C([α,β]), where [α,β] is a bounded real interval. The asymptotic behaviour and regularity with respect to the space variable are also investigated.
LA - eng
KW - analytic semigroups; Ventcel's boundary conditions
UR - http://eudml.org/doc/216471
ER -

References

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  5. [5] M. Campiti and G. Metafune, Ventcel's boundary conditions and analytic semigroups, Arch. Math. (Basel), to appear. Zbl0909.34051
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  9. [9] A. Favini and S. Romanelli, Analytic semigroups on C([0,1]) generated by some classes of second order differential operators, Semigroup Forum, to appear. Zbl0910.47034
  10. [10] W. Feller, Two singular diffusion problems, Ann. of Math. 54 (1951), 173-182. Zbl0045.04901
  11. [11] W. Feller, The parabolic differential equations and the associated semi-groups of transformations, ibid. 55 (1952), 468-519. Zbl0047.09303
  12. [12] G. Fichera, On a degenerate evolution problem, in: Partial Differential Equations with Real Analysis, H. Begeher and A. Jeffrey (eds.), Pitman Res. Notes Math. Ser. 263, Longman, 1992, 15-42. Zbl0806.35097
  13. [13] R. Nagel (ed.), One-Parameter Semigroups of Positive Operators, Springer, 1986. Zbl0585.47030
  14. [14] K. Taira, On the existence of Feller semigroups with boundary conditions, II, J. Funct. Anal. 129 (1995), 108-131. Zbl0898.47032
  15. [15] C. A. Timmermans, On C 0 -semigroups in a space of bounded continuous functions in the case of entrance or natural boundary points, in: Approximation and Optimization, J. A. Gómez Fernández et al. (eds.), Lecture Notes in Math. 1354, Springer, 1988, 209-216. 

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