Nonlinear parabolic equations with natural growth in general domains

A. Dall'aglio; D. Giachetti; J.-P. Puel

Bollettino dell'Unione Matematica Italiana (2005)

  • Volume: 8-B, Issue: 3, page 653-683
  • ISSN: 0392-4041

Abstract

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We prove an existence result for a class of parabolic problems whose principal part is the p -Laplace operator or a more general Leray-Lions type operator, and featuring an additional first order term which grows like | ∇ u | p . Here the spatial domain can have infinite measure, and the data may be not regular enough to ensure the boundedness of solutions. As a consequence, solutions are obtained in a class of functions with exponential integrability. An existence result of bounded solutions is also given under additional hypotheses.

How to cite

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Dall'aglio, A., Giachetti, D., and Puel, J.-P.. "Nonlinear parabolic equations with natural growth in general domains." Bollettino dell'Unione Matematica Italiana 8-B.3 (2005): 653-683. <http://eudml.org/doc/195326>.

@article{Dallaglio2005,
abstract = {We prove an existence result for a class of parabolic problems whose principal part is the $p$-Laplace operator or a more general Leray-Lions type operator, and featuring an additional first order term which grows like $|\nabla u |^\{p\}$. Here the spatial domain can have infinite measure, and the data may be not regular enough to ensure the boundedness of solutions. As a consequence, solutions are obtained in a class of functions with exponential integrability. An existence result of bounded solutions is also given under additional hypotheses.},
author = {Dall'aglio, A., Giachetti, D., Puel, J.-P.},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {653-683},
publisher = {Unione Matematica Italiana},
title = {Nonlinear parabolic equations with natural growth in general domains},
url = {http://eudml.org/doc/195326},
volume = {8-B},
year = {2005},
}

TY - JOUR
AU - Dall'aglio, A.
AU - Giachetti, D.
AU - Puel, J.-P.
TI - Nonlinear parabolic equations with natural growth in general domains
JO - Bollettino dell'Unione Matematica Italiana
DA - 2005/10//
PB - Unione Matematica Italiana
VL - 8-B
IS - 3
SP - 653
EP - 683
AB - We prove an existence result for a class of parabolic problems whose principal part is the $p$-Laplace operator or a more general Leray-Lions type operator, and featuring an additional first order term which grows like $|\nabla u |^{p}$. Here the spatial domain can have infinite measure, and the data may be not regular enough to ensure the boundedness of solutions. As a consequence, solutions are obtained in a class of functions with exponential integrability. An existence result of bounded solutions is also given under additional hypotheses.
LA - eng
UR - http://eudml.org/doc/195326
ER -

References

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