### Higher integrability for weak solutions of higher order degenerate parabolic systems.

Bögelein, Verena (2008)

Annales Academiae Scientiarum Fennicae. Mathematica

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Bögelein, Verena (2008)

Annales Academiae Scientiarum Fennicae. Mathematica

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Wojciech Zajączkowski (1996)

Banach Center Publications

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Existence of weak solutions and an ${L}_{\infty}$-estimate are shown for nonlinear nondegenerate parabolic systems with linear growth conditions with respect to the gradient. The ${L}_{\infty}$-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.

Voisei, Mircea D. (2005)

Electronic Journal of Differential Equations (EJDE) [electronic only]

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Pudełko, Anna (2004)

Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica

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Ronto, A.N., Rontó, M., Samoilenko, A.M., Trofimchuk, S.I. (2001)

Georgian Mathematical Journal

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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 ${L}_{\infty}$-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.

D. Bainov, Zdzisław Kamont, E. Minchev (1996)

Applicationes Mathematicae

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Theorems on differential inequalities generated by an initial-boundary value problem for impulsive parabolic functional differential equations are considered. Comparison results implying uniqueness criteria are proved.

M. Medveď (1991)

Annales Polonici Mathematici

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We prove several results on lower bounds for the periods of periodic solutions of some classes of functional-differential equations in Hilbert and Banach spaces and difference inclusions in Hilbert spaces.

Nguetseng, Gabriel, Woukeng, Jean Louis (2004)

Electronic Journal of Differential Equations (EJDE) [electronic only]

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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\to \infty $. Finally, we obtain the asymptotic behavior near the blow-up time of certain blow-up solutions and describe their blow-up set.

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.

Jangveladze, T., Kiguradze, Z. (2002)

Georgian Mathematical Journal

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