Nonlinear parabolic equations with natural growth in general domains
Bollettino della Unione matematica italiana, Série 8, 8B (2005) no. 3, pp. 653-683
Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica
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.
@article{BUMI_2005_8_8B_3_a8,
author = {Dall'aglio, A. and Giachetti, D. and Puel, J.-P.},
title = {Nonlinear parabolic equations with natural growth in general domains},
journal = {Bollettino della Unione matematica italiana},
pages = {653--683},
publisher = {mathdoc},
volume = {Ser. 8, 8B},
number = {3},
year = {2005},
zbl = {1117.35035},
mrnumber = {MR2182422},
language = {en},
url = {http://geodesic.mathdoc.fr/item/BUMI_2005_8_8B_3_a8/}
}
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 della Unione matematica italiana PY - 2005 SP - 653 EP - 683 VL - 8B IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/BUMI_2005_8_8B_3_a8/ LA - en ID - BUMI_2005_8_8B_3_a8 ER -
%0 Journal Article %A Dall'aglio, A. %A Giachetti, D. %A Puel, J.-P. %T Nonlinear parabolic equations with natural growth in general domains %J Bollettino della Unione matematica italiana %D 2005 %P 653-683 %V 8B %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/BUMI_2005_8_8B_3_a8/ %G en %F BUMI_2005_8_8B_3_a8
Dall'aglio, A.; Giachetti, D.; Puel, J.-P. Nonlinear parabolic equations with natural growth in general domains. Bollettino della Unione matematica italiana, Série 8, 8B (2005) no. 3, pp. 653-683. http://geodesic.mathdoc.fr/item/BUMI_2005_8_8B_3_a8/