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Displaying similar documents to “Doubling properties for second order parabolic equations.”

Existence of a classical solution for linear parabolic systems of nondivergence form

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.

Some (new) counterexamples of parabolic systems

Jana Stará, Oldřich John (1995)

Commentationes Mathematicae Universitatis Carolinae

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We give examples of parabolic systems (in space dimension n ≥ 3 ) having a solution with real analytic initial and boundary values which develops the discontinuity in the interior of the parabolic cylinder.