On the abstract Cauchy problem in the case of constant domains

Paolo Acquistapace; Brunello Terreni

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1984)

  • Volume: 76, Issue: 1, page 7-13
  • ISSN: 1120-6330

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Acquistapace, Paolo, and Terreni, Brunello. "On the abstract Cauchy problem in the case of constant domains." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 76.1 (1984): 7-13. <http://eudml.org/doc/287270>.

@article{Acquistapace1984,
author = {Acquistapace, Paolo, Terreni, Brunello},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {first order differential equation; evolution non-autonomous equation; analytic semigroups; Hölder-continuity},
language = {eng},
month = {1},
number = {1},
pages = {7-13},
publisher = {Accademia Nazionale dei Lincei},
title = {On the abstract Cauchy problem in the case of constant domains},
url = {http://eudml.org/doc/287270},
volume = {76},
year = {1984},
}

TY - JOUR
AU - Acquistapace, Paolo
AU - Terreni, Brunello
TI - On the abstract Cauchy problem in the case of constant domains
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1984/1//
PB - Accademia Nazionale dei Lincei
VL - 76
IS - 1
SP - 7
EP - 13
LA - eng
KW - first order differential equation; evolution non-autonomous equation; analytic semigroups; Hölder-continuity
UR - http://eudml.org/doc/287270
ER -

References

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  1. ACQUISTAPACE, P. and TERRENI, B. (1984) - Some existence and regularity results for abstract non-autonomous parabolic equations, «J. Math. Anal. Appl.». 99, 9-64. Zbl0555.34051
  2. BAILLON, J.B. (1980) - Caractère borné de certains générateurs de semi-groupes linéaires dans les espaces de Banach, «C.R. Acad. Sc. Paris», 290 (28 avril 1980), série A, 757-760. Zbl0436.47027
  3. BUTZER, P.L. and BERENS, H. (1967) - Semi-groups of operators and approximation, Springer Verlag, Berlin. Zbl0164.43702
  4. CRANDALL, M.G. and PAZY, A. (1969) - On the differentiability of weak solutions of a differential equation in Banach space, «J. Math. Mech.», 18, 1007-1016. Zbl0177.42901
  5. DA PRATO, G. and GRISVARD, P. (1975) - Sommes d'opérateurs linéaires et équations différentielles opérationnelles, «J. Math. Pures Appl.», 54, 305-387. 
  6. DA PRATO, G. and GRISVARD, P. (1979) - Equations d'évolution abstraites non linéaires de type parabolique, «Ann. Mat. Pura Appl.» (4) 120, 329-396. Zbl0471.35036
  7. DA PRATO, G. and SINESTRARI, E. (1982) - Holder regularity for non-autonomous abstract parabolic equations, «Israel J. Math.», 42, 1-19. Zbl0495.47031
  8. POULSEN, E.T. (1965) - Evolutionsgleichungen in Banach Räumen, «Math. Z.», 90, 289-309. 
  9. SINESTRARI, E. (1981) - On the solutions of the inhomogeneous evolution equations in Banach spaces, «Atti Acc. Naz. Lincei, Rend. Cl. Sc. Fis. Mat. Nat.», 70, 12-17. Zbl0507.47027
  10. SINESTRARI, E. (1981) - Abstract semi-linear equations in Banach spaces, «Atti Acc. Naz. Lincei, Rend. Cl. Sc. Fis. Mat. Nat.», 70, 81-86. Zbl0507.47026
  11. SOBOLEVSKII, P.E. (1961) - On equations of parabolic type in Banach space, «Trudy Moscow Mat. Obsc.», 10, 297-350 (Russian); english translation: «Amer. Math. Soc. Transl.», 49, 1-62. 
  12. TANABE, H. (1960) - On the equations of evolution in a Banach space, «Osaka Math. J.», 12, 363-376. Zbl0098.31301
  13. TANABE, H. (1979) - Equations of evolution, Pitman, London. 
  14. TRAVIS, C.C. (1981) - Differentiability of weak solutions to an abstract inhomogeneous differential equation, «Proc. Amer. Math. Soc.», 28, 425-430. Zbl0484.34044

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