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.
In questo articolo si dimostra un risultato di esistenza per una classe di problemi parabolici la cui parte principale è l'operatore $p$-Laplaciano, oppure un operatore più generale del tipo di Leray-Lions, e in cui compare un termine aggiuntivo del primo ordine che cresce come $|\nabla u |^{p}$. Il dominio spaziale in cui si risolve il problema può avere misura infinita, e i dati possono non avere la regolarità necessaria per garantire la limitatezza delle soluzioni. Di conseguenza, si ottengono soluzioni in una classe di funzioni con integrabilità esponenziale. Sotto ipotesi più forti, si prova l'esistenza di soluzioni limitate.
@article{BUMI_2005_8_8B_3_653_0,
author = {A. Dall'aglio and D. Giachetti and J.-P. Puel},
title = {Nonlinear parabolic equations with natural growth in general domains},
journal = {Bollettino dell'Unione Matematica Italiana},
volume = {8-A},
year = {2005},
pages = {653-683},
zbl = {1117.35035},
mrnumber = {2182422},
language = {en},
url = {http://dml.mathdoc.fr/item/BUMI_2005_8_8B_3_653_0}
}
Dall'aglio, A.; Giachetti, D.; Puel, J.-P. Nonlinear parabolic equations with natural growth in general domains. Bollettino dell'Unione Matematica Italiana, Tome 8-A (2005) pp. 653-683. http://gdmltest.u-ga.fr/item/BUMI_2005_8_8B_3_653_0/
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