Displaying similar documents to “Decay rates for solutions of degenerate parabolic systems.”

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.

Smooth solutions of systems of quasilinear parabolic equations

Alain Bensoussan, Jens Frehse (2002)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider in this article diagonal parabolic systems arising in the context of stochastic differential games. We address the issue of finding smooth solutions of the system. Such a regularity result is extremely important to derive an optimal feedback proving the existence of a Nash point of a certain class of stochastic differential games. Unlike in the case of scalar equation, smoothness of solutions is not achieved in general. A special structure of the nonlinear hamiltonian seems...