Volterra integrodifferential equations of parabolic type of higher order in time in L p spaces

Davide Guidetti

Rendiconti del Seminario Matematico della Università di Padova (2000)

  • Volume: 103, page 65-111
  • ISSN: 0041-8994

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Guidetti, Davide. "Volterra integrodifferential equations of parabolic type of higher order in time in $L^p$ spaces." Rendiconti del Seminario Matematico della Università di Padova 103 (2000): 65-111. <http://eudml.org/doc/108529>.

@article{Guidetti2000,
author = {Guidetti, Davide},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {Volterra integrodifferential equation; Banach space; analytic semigroup; evolution operator},
language = {eng},
pages = {65-111},
publisher = {Seminario Matematico of the University of Padua},
title = {Volterra integrodifferential equations of parabolic type of higher order in time in $L^p$ spaces},
url = {http://eudml.org/doc/108529},
volume = {103},
year = {2000},
}

TY - JOUR
AU - Guidetti, Davide
TI - Volterra integrodifferential equations of parabolic type of higher order in time in $L^p$ spaces
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 2000
PB - Seminario Matematico of the University of Padua
VL - 103
SP - 65
EP - 111
LA - eng
KW - Volterra integrodifferential equation; Banach space; analytic semigroup; evolution operator
UR - http://eudml.org/doc/108529
ER -

References

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  1. [1] P. Acquistapace, Existence and maximal time regularity for linear parabolic integrodifferential equations, Journ. Int. Eq., 10 (1985), pp. 5-43. Zbl0584.45012MR831233
  2. [2] P. Acquistapace - B. Terreni, Linear parabolic equations in Banach spaces with variable domain but constant interpolation spaces, Ann. Sc. Norm. Sup. Pisa, ser. IV, 13 (1986), pp. 75-107. Zbl0612.34057MR863636
  3. [3] P. Acquistapace - B. Terreni, Existence and sharp regularity results for linear parabolic non-autonomous integro-differential equations, Israel Journ. Math. vol. 53, n. 3 (1986), pp. 257-303. Zbl0603.45019MR852481
  4. [4] G. Di Blasio, Nonautonomous integrodifferential equations in Lp spaces, Journ. Int. Eq., 10 (1985), pp. 111-121. Zbl0585.45006MR831238
  5. [5] D. Guidetti, Abstract linear parabolic problems with nonhomogeneous boundary conditions, in Semigroup theory and evolution equations, (ed. P. Clement, E. Mitidieri, B. de Pagter), Lec. Notes in Pure and Appl. Math. vol. 135, Marcel Dekker Inc. (1991). Zbl0781.35024MR1164653
  6. [6] D. Guidetti, On boundary value problems for parabolic equations of higher order in time, Journ. Diff. Eq., vol. 124, n. 1 (1996), pp. 1-26. Zbl0844.35039MR1368060
  7. [7] T. Kato - H. Tanabe, On the abstract evolution equation, Osaka Math. Journ.14 (1962), pp. 107-133. Zbl0106.09302MR140954
  8. [8] S.G. Krein, Linear differential equations in Banach spaces, Translations of Mathematical Monographs, vol. 29 (1971). MR342804
  9. [9] A. Lunardi, Regular solutions for time dependent abstract integrodifferential equations with singular kernel, Journ. Math. Anal. Appl., 130 (1988), 1-21. Zbl0638.45007MR926824
  10. [10] A. Lunardi - E. Sinestrari, Ca-regularity for nonautonomous linear integrodifferential equations, J. Diff. Eq., 63 (1986), pp. 88-116. Zbl0596.45019MR840594
  11. [11] J. Prüss, On resolvent operators for linear integrodifferential equations of Volterra type, Journ. Integral Eq., 5 (1983), 211-236. Zbl0518.45008MR702432
  12. [12] H. Tanabe, Volterra integro-differential equations of parabolic type of higher order in t, Journ. Fac. Science, Tokyo Univ., Sec. IA, vol. 34, n. 1 (1987), pp. 115-125. Zbl0628.45008MR882127
  13. [13] H. Tanabe, On fundamental solutions of linear parabolic equations of higher order in time and associated Volterra equations, Journ. Diff. Eq., 73 (1988), 288-308. Zbl0673.35042MR943944
  14. [TR] H. Triebel, Theory of function spaces, Monographs in Mathematics, Birkhäuser (1983). Zbl0546.46027MR781540

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