Some problems of parabolic type with discontinuous nonlinearities on convex constraints

Marlène Frigon; Antonio Marino; Claudio Saccon

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1990)

  • Volume: 1, Issue: 1, page 41-52
  • ISSN: 1120-6330

Abstract

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We study semilinear equations and inequalities of parabolic type with discontinuous nonlinearities, possibly subjected to convex or even nonconvex constraint conditions. To prove some existence theorems we regard the solutions as «curves of maximal relaxed slope» for a suitable functional on the given constraint.

How to cite

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Frigon, Marlène, Marino, Antonio, and Saccon, Claudio. "Some problems of parabolic type with discontinuous nonlinearities on convex constraints." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 1.1 (1990): 41-52. <http://eudml.org/doc/244256>.

@article{Frigon1990,
abstract = {We study semilinear equations and inequalities of parabolic type with discontinuous nonlinearities, possibly subjected to convex or even nonconvex constraint conditions. To prove some existence theorems we regard the solutions as «curves of maximal relaxed slope» for a suitable functional on the given constraint.},
author = {Frigon, Marlène, Marino, Antonio, Saccon, Claudio},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Curves of maximal slope; Partial differential equations; Discontinuity; Nonconvex constraints; semilinear; discontinuous nonlinearity; nonconvex constraints; curves of maximal relaxed slope},
language = {eng},
month = {2},
number = {1},
pages = {41-52},
publisher = {Accademia Nazionale dei Lincei},
title = {Some problems of parabolic type with discontinuous nonlinearities on convex constraints},
url = {http://eudml.org/doc/244256},
volume = {1},
year = {1990},
}

TY - JOUR
AU - Frigon, Marlène
AU - Marino, Antonio
AU - Saccon, Claudio
TI - Some problems of parabolic type with discontinuous nonlinearities on convex constraints
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1990/2//
PB - Accademia Nazionale dei Lincei
VL - 1
IS - 1
SP - 41
EP - 52
AB - We study semilinear equations and inequalities of parabolic type with discontinuous nonlinearities, possibly subjected to convex or even nonconvex constraint conditions. To prove some existence theorems we regard the solutions as «curves of maximal relaxed slope» for a suitable functional on the given constraint.
LA - eng
KW - Curves of maximal slope; Partial differential equations; Discontinuity; Nonconvex constraints; semilinear; discontinuous nonlinearity; nonconvex constraints; curves of maximal relaxed slope
UR - http://eudml.org/doc/244256
ER -

References

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  9. DE GIORGI, E. - MARINO, A. - TOSQUES, M., Problemi di evoluzione in spazi metrici e curve di massima pendenza. Atti Acc. Lincei Rend. fis., s. 8, vol. 68, 1980, 180-187. Zbl0465.47041MR636814
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