Displaying similar documents to “A minmax problem for parabolic systems with competitive interactions.”

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...