Regularity for doubly nonlinear parabolic equations
Ivanov, Alexander V.
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Ivanov, Alexander V.
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Masashi Misawa (2004)
Commentationes Mathematicae Universitatis Carolinae
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We prove the unique existence of a classical solution for a linear parabolic system of nondivergence and nondiagonal form. The key ingredient is to combine the energy estimates with Schauder estimates and to obtain a uniform boundedness of a solution.
Di Benedetto, Emmanuele
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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.