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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Pudełko, Anna (2004)
Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica
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Wojciech Zajączkowski (1996)
Banach Center Publications
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Existence of weak solutions and an -estimate are shown for nonlinear nondegenerate parabolic systems with linear growth conditions with respect to the gradient. The -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.
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 -estimate for weak solutions is shown under additional restrictive growth conditions. Finally, -estimates for weakly nondiagonal systems (where nondiagonal elements are absorbed by diagonal ones) are proved. The -estimates are obtained by the Di Benedetto methods.
Bychowska, A. (2002)
Georgian Mathematical Journal
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Arina A. Arkhipova (2001)
Commentationes Mathematicae Universitatis Carolinae
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We prove local in time solvability of the nonlinear initial-boundary problem to nonlinear nondiagonal parabolic systems of equations (multidimensional case). No growth restrictions are assumed on generating the system functions. In the case of two spatial variables we construct the global in time solution to the Cauchy-Neumann problem for a class of nondiagonal parabolic systems. The solution is smooth almost everywhere and has an at most finite number of singular points.
Kavitha, V., Arjunan, M.Mallika, Ravichandran, C. (2011)
The Journal of Nonlinear Sciences and its Applications
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Leszczyński, Henryk (2000)
Georgian Mathematical Journal
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Bouziani, A., Merazga, N. (2007)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
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Jaruszewska-Walczak, Danuta (2005)
Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica
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