Smoothness in fractional evolution equations and conservation laws

Gustaf Gripenberg; Philippe Clément; Stig-Olof Londen

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2000)

  • Volume: 29, Issue: 1, page 231-251
  • ISSN: 0391-173X

How to cite

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Gripenberg, Gustaf, Clément, Philippe, and Londen, Stig-Olof. "Smoothness in fractional evolution equations and conservation laws." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 29.1 (2000): 231-251. <http://eudml.org/doc/84404>.

@article{Gripenberg2000,
author = {Gripenberg, Gustaf, Clément, Philippe, Londen, Stig-Olof},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {existence of regular solutions; fractional conservation laws; entropy solutions},
language = {eng},
number = {1},
pages = {231-251},
publisher = {Scuola normale superiore},
title = {Smoothness in fractional evolution equations and conservation laws},
url = {http://eudml.org/doc/84404},
volume = {29},
year = {2000},
}

TY - JOUR
AU - Gripenberg, Gustaf
AU - Clément, Philippe
AU - Londen, Stig-Olof
TI - Smoothness in fractional evolution equations and conservation laws
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 2000
PB - Scuola normale superiore
VL - 29
IS - 1
SP - 231
EP - 251
LA - eng
KW - existence of regular solutions; fractional conservation laws; entropy solutions
UR - http://eudml.org/doc/84404
ER -

References

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  1. [1] Ph. CLÉMENT - G. Gripenberg - S-O. Londen, Schauder estimates for equations with fractional derivatives, Trans. Amer. Math. Soc., to appear. Zbl0947.35023MR1675170
  2. [2] PH. Clément - G. Gripenberg - S-O. Londen, Hölder regularity for a linear fractional evolution equation, In: "Topics in Nonlinear Analysis", J. Escher - G. Simonett (eds.), vol. 35, Birkhäuser, Basel, 1999. Zbl0920.35004MR1725566
  3. [3] B. Cockburn - G. Gripenberg - S-O. Londen, On convergence to entropy solutions of a single conservation law, J. Differential Equations128 (1996), 206-251. Zbl0859.35073MR1392401
  4. [4] M.G. Crandall, The semigroup approach to first order quasilinear equations in several space variables, Israel J. Math.12 (1972), 108-132. Zbl0246.35018MR316925
  5. [5] G. Da Prato - M. Iannelli, Linear integro-differential equations in Banach spaces, Rend. Sem. Mat. Univ. Padova62 (1980), 207-219. Zbl0451.45014MR582951
  6. [6] G. Da Prato - M. Iannelli - E. Sinestrari, Temporal regularity for a class of integrodifferential equations in Banach spaces, Boll. Un. Mat. Ital.2 (1983), 171-185. Zbl0527.45005MR718369
  7. [7] G. Da Prato - M. Iannelli - E. Sinestrari, Regularity of solutions of a class of linear integrodifferential equations in Banach spaces, J. Integral Equations8 (1985), 27-40. Zbl0576.45011MR771750
  8. [8] E. Godlewski - P.-A. Raviart, "Hyperbolic systems of conservation laws", Ellipses, Paris, 1991. Zbl0768.35059MR1304494
  9. [9] G. Gripenberg, An abstract nonlinear Volterra equation, Israel J. Math.34 (1979), 198-212. Zbl0433.45017MR570881
  10. [10] G. Gripenberg, Volterra integro-differential equations with accretive nonlinearity, J. Differential Equations60 (1985), 57-79. Zbl0575.45013MR808257
  11. [11] G. Gripenberg - S-O. Londen, Fractional derivatives and smoothing in nonlinear conservation laws, Differential Integral Equations8 (1995), 1961-1976. Zbl0885.45005MR1348960
  12. [12] J. Prüss, "Evolutionary integral equations and applications", Birkhäuser, Basel, 1995. Zbl0784.45006MR1238939
  13. [13] A. Lunardi, "Analytic semigroups and optimal regularity in parabolic problems", Birkhäuser, Basel, 1995. Zbl0816.35001MR1329547
  14. [14] D. Serre, "Systems of conservation laws 1", Cambridge University Press, Cambridge, 1999. Zbl0930.35001MR1707279
  15. [15] A. Zygmund, "Trigonometric series II", Cambridge University Press, Cambridge, 1959. Zbl0085.05601MR107776

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