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Displaying similar documents to “Periodic solutions in superlinear parabolic problems.”

L -estimates for solutions of nonlinear parabolic systems with gradient linear growth

Wojciech Zajączkowski (1996)

Banach Center Publications

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Existence of weak solutions and an L -estimate are shown for nonlinear nondegenerate parabolic systems with linear growth conditions with respect to the gradient. The L -estimate is proved for equations with coefficients continuous with respect to x and t in the general main part, and for diagonal systems with coefficients satisfying the Carathéodory condition.

L -estimate for solutions of nonlinear parabolic systems

Wojciech Zajączkowski (1996)

Banach Center Publications

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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 -estimate for weak solutions is shown under additional restrictive growth conditions. Finally, L -estimates for weakly nondiagonal systems (where nondiagonal elements are absorbed by diagonal ones) are proved. The L -estimates are obtained by the Di Benedetto methods.

On blow-up and asymptotic behavior of solutions to a nonlinear parabolic equation of second order with nonlinear boundary conditions

Théodore K. Boni (1999)

Commentationes Mathematicae Universitatis Carolinae

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We obtain some sufficient conditions under which solutions to a nonlinear parabolic equation of second order with nonlinear boundary conditions tend to zero or blow up in a finite time. We also give the asymptotic behavior of solutions which tend to zero as t . Finally, we obtain the asymptotic behavior near the blow-up time of certain blow-up solutions and describe their blow-up set.

Monotone method for nonlinear second order periodic boundary value problems with Carathéodory functions

Ming-Xing Wang, Alberto Cabada, Juan J. Nieto (1993)

Annales Polonici Mathematici

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The purpose of this paper is to study the periodic boundary value problem -u''(t) = f(t,u(t),u'(t)), u(0) = u(2π), u'(0) = u'(2π) when f satisfies the Carathéodory conditions. We show that a generalized upper and lower solution method is still valid, and develop a monotone iterative technique for finding minimal and maximal solutions.