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1996 | 33 | 1 | 465-490
Tytuł artykułu

$L_∞$-estimate for solutions of nonlinear parabolic systems

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Słowa kluczowe
Rocznik
Tom
33
Numer
1
Strony
465-490
Opis fizyczny
Daty
wydano
1996
Bibliografia
  • [1] H, W. Alt and S. Luckhaus, Quasilinear elliptic-parabolic differential equations, Math. Z. 183 (1983), 311-341.
  • [2] J. P. Aubin and I. Ekeland, Applied Nonlinear Analysis, Wiley, New York, 1984.
  • [3] E. Di Benedetto, Degenerate Parabolic Eequations, Springer, 1993.
  • [4] J. Filo and J. Kacur, Local existence of general nonlinear parabolic systems, Comenius Univ., Faculty of Math. and Phys., Preprint No. M5-91, July 1991, Bratislava.
  • [5] J. Kacur, On a solution of degenerate elliptic-parabolic systems in Orlicz-Sobolev spaces I, Math. Z. 203 (1990), 153-171.
  • [6] O. A. Ladyzhenskaya, V. A. Solonnikov, and N. N. Uraltseva, Linear and Quasilinear Equations of Parabolic Type, Amer. Math. Soc., Providence, R.I., 1968.
  • [7] O. A. Ladyzhenskaya and N. N. Uraltseva, Linear and Quasilinear Equations of Elliptic Type, Nauka, Moscow, 1973 (in Russian).
  • [8] D. Wrzosek, The nonstationary semiconductor model with bounded convective velocity and generation/recombination term, in: Mathematical Modelling and Simulation of Electrical Circuits and Semiconductor Devices, Internat. Ser. Numer. Math. 117, Birkhäuser, Basel, 1994, 293-313.
  • [9] E. Zadrzyńska and W. M. Zajączkowski, On existence of solutions of mixed problems for parabolic systems, Topol. Methods Nonlinear Anal. 2 (1993), 125-145.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-bcpv33z1p465bwm
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