Geodesic
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. 
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     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/}
}
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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/