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Non well posedness of parabolic equations with supercritical nonlinearities

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Arrieta Algarra, José María and Rodríguez Bernal, Aníbal (2004) Non well posedness of parabolic equations with supercritical nonlinearities. Communications in contemporary mathematics, 6 (5). pp. 733-764. ISSN 0219-1997

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Official URL: http://www.worldscientific.com/doi/pdf/10.1142/S0219199704001495


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Abstract

In this paper we show that several known critical exponents for nonlinear parabolic problems axe optimal in the sense that supercritical problems are ill posed in a strong sense. We also give an answer to an open problem proposed by Brezis and Cazenave in [9], concerning the behavior of the existence time for critical problems. Our results cover nonlinear heat equations including the case of nonlinear boundary conditions and weigthed spaces settings. In the latter case we show that in some cases the critical exponent is equal to one.


Item Type:Article
Uncontrolled Keywords:Critical exponents; Non-well-posedness; Nonlinear heat equations; Nonlinear boundary conditions; Weighted spaces proper minimal solutions
Subjects:Sciences > Mathematics > Differential equations
ID Code:17736
Deposited On:17 Jan 2013 09:14
Last Modified:12 Dec 2018 15:07

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