Parabolic equations with multiple singularities
Di Benedetto, Emmanuele
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Di Benedetto, Emmanuele
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Ivanov, Alexander V.
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S.N. Antonsev, J.I. Díaz (2009)
RACSAM
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Taranets, R.M. (2006)
Sibirskij Matematicheskij Zhurnal
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Anatolii S. Kalashnikov (1997)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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The paper contains conditions ensuring instantaneous shrinking of the support for solutions to semilinear parabolic equations with compactly supported coefficients of nonlinear terms and reaction-diffusion systems.
Winkler, M. (2003)
Acta Mathematica Universitatis Comenianae. New Series
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Changchun Liu (2013)
Annales Polonici Mathematici
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We consider an initial-boundary problem for a sixth order nonlinear parabolic equation, which arises in oil-water-surfactant mixtures. Using Schauder type estimates and Campanato spaces, we prove the global existence of classical solutions for the problem in two space dimensions.