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1998 | 127 | 3 | 251-276
Tytuł artykułu

Analyticity for some degenerate one-dimensional evolution equations

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Słowa kluczowe
Czasopismo
Rocznik
Tom
127
Numer
3
Strony
251-276
Opis fizyczny
Daty
wydano
1998
otrzymano
1996-11-18
poprawiono
1997-08-11
Twórcy
autor
  • Dipartimento di Matematica, Università di Lecce, C.P.193 73100 Lecce, Italy, metafune@le.infn.it
Bibliografia
  • [1] M. Abramowitz and I. Stegun, Handbook of Mathematical Functions, Dover, 1972.
  • [2] S. Angenent, Local existence and regularity for a class of degenerate parabolic equations, Math. Ann. 280 (1988), 465-482.
  • [3] A. Attalienti and S. Romanelli, On some classes of analytic semigroups on C([a,b]) related to R- or Γ-admissible mappings, in: Evolution Equations, G. Ferreyra, G. Goldstein and F. Neubrander (eds.), Lecture Notes in Pure and Appl. Math. 168, Dekker, 1995, 29-34.
  • [4] H. Brezis, W. Rosenkrantz and B. Singer, On a degenerate elliptic-parabolic equation occurring in the theory of probability, Comm. Pure Appl. Math. 24 (1971), 395-416.
  • [5] M. Campiti and G. Metafune, Ventcel's boundary conditions and analytic semigroups, Arch. Math. (Basel), to appear.
  • [6] M. Campiti, G. Metafune and D. Pallara, Degenerate self-adjoint evolution equations on the unit interval, Semigroup Forum, to appear.
  • [7] P. Clément and C. A. Timmermans, On $C_0$-semigroups generated by differential operators satisfying Ventcel's boundary conditions, Indag. Math. 89 (1986), 379-387.
  • [8] A. Favini, J. Goldstein and S. Romanelli, Analytic semigroups on $L_w^p(0,1)$ generated by some classes of second order differential operators, preprint, 1996.
  • [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.
  • [10] W. Feller, Two singular diffusion problems, Ann. of Math. 54 (1951), 173-182.
  • [11] W. Feller, The parabolic differential equations and the associated semi-groups of transformations, ibid. 55 (1952), 468-519.
  • [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.
  • [13] R. Nagel (ed.), One-Parameter Semigroups of Positive Operators, Springer, 1986.
  • [14] K. Taira, On the existence of Feller semigroups with boundary conditions, II, J. Funct. Anal. 129 (1995), 108-131.
  • [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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Bibliografia
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bwmeta1.element.bwnjournal-article-smv127i3p251bwm
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