Existence and regularity results for abstract non autonomous parabolic equations

Paolo Acquistapace; Brunello Terreni

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1982)

  • Volume: 72, Issue: 6, page 322-329
  • ISSN: 1120-6330

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Acquistapace, Paolo, and Terreni, Brunello. "Existence and regularity results for abstract non autonomous parabolic equations." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 72.6 (1982): 322-329. <http://eudml.org/doc/286973>.

@article{Acquistapace1982,
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 = {evolution equations; Banach spaces; analytic semigroups; Cauchy problem},
language = {eng},
month = {6},
number = {6},
pages = {322-329},
publisher = {Accademia Nazionale dei Lincei},
title = {Existence and regularity results for abstract non autonomous parabolic equations},
url = {http://eudml.org/doc/286973},
volume = {72},
year = {1982},
}

TY - JOUR
AU - Acquistapace, Paolo
AU - Terreni, Brunello
TI - Existence and regularity results for abstract non autonomous parabolic equations
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1982/6//
PB - Accademia Nazionale dei Lincei
VL - 72
IS - 6
SP - 322
EP - 329
LA - eng
KW - evolution equations; Banach spaces; analytic semigroups; Cauchy problem
UR - http://eudml.org/doc/286973
ER -

References

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  1. Baillon, J.B. (1980) - Caractère borné de certains générateurs de semigroupes linéaires dans les espaces de Banach, «C. R. Acad. Sc. Paris», 290, (28 avril) série A 757-760. Zbl0436.47027
  2. Butzer, P.L. and Berens, H. (1967) - Semigroups of operators and approximation, Springer VerlagBerlin. Zbl0164.43702
  3. 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
  4. Da Prato, G. and Grisvard, P. (1975) - Sommes d 'opérateurs linéaires et équations différentielles opérationnelles, «J. Math. Pures Appl.», 54305-387. Zbl0315.47009
  5. 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
  6. Da Prato, G. and Sinestrari, E. - Hölder regularity for non autonomous abstract parabolic equations, to appear in «Israel J. Math.». Zbl0495.47031
  7. Kato, T. (1961) - Abstract evolution equations of parabolic type in Banach and Hilbert spaces, «Nagoya J. Math.», 19, 93-125. Zbl0114.06102
  8. Kato, T. and Tanabe, H. (1962) - On the abstract evolution equations, «Osaka Math. J.», 14, 107-133. Zbl0106.09302
  9. Poulsen, E.T. (1965) - Evolutionsgleichungen in Banach Raumen, «Math. Z.», 90, 289-309. Zbl0141.13102
  10. Sinestrari, E. (1981) - On the solutions of the inhomogeneous evolution equations in Banach spaces, to appear in «Atti Acc. Naz. Lincei Rend. Cl. Sc. Fis. Mat. Nat.», LXX. 
  11. Sinestrari, E. (1981) - Abstract semilinear equations in Banach spaces, to appear in «Atti Acc. Naz. Lincei Rend. Cl. Sc. Fis. Mat. Nat.», LXX. Zbl0507.47026
  12. Sobolevski, P.E. (1961) - Parabolic equations in a Banach space with an unbounded variable operator, a fractional power of which has a constant domain of definition, «Dokl. Akad. Nauk», 138, 59-62; English translation «Soviet Math. Dokl.», 2, 545-548. 
  13. Tanabe, H. (1969) - Equations of evolution, PitmanLondon. 
  14. Travis, C.C. (1981) - Differentiability of weak solutions to an abstract inhomogeneous differential equation, «Proc. Amer. Math. Soc.», 28, 425-430. Zbl0484.34044
  15. Yagi, A. (1977) - On the abstract evolution equations of parabolic type, «Osaka J. Math.», 14, 557-568. Zbl0371.47037

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