EUDML | Existence of solutions of the Cauchy problem for semilinear infinite systems of parabolic differential-functional equations.

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Displaying similar documents to “Existence of solutions of the Cauchy problem for semilinear infinite systems of parabolic differential-functional equations.”

$L_{\infty}$ -estimate for solutions of nonlinear parabolic systems

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We prove existence of weak solutions to nonlinear parabolic systems with p-Laplacians terms in the principal part. Next, in the case of diagonal systems an $L_{\infty}$ -estimate for weak solutions is shown under additional restrictive growth conditions. Finally, $L_{\infty}$ -estimates for weakly nondiagonal systems (where nondiagonal elements are absorbed by diagonal ones) are proved. The $L_{\infty}$ -estimates are obtained by the Di Benedetto methods.

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