L ∞ -estimate for solutions of nonlinear parabolic systems

Wojciech Zajączkowski

Banach Center Publications (1996)

  • Volume: 33, Issue: 1, page 465-490
  • ISSN: 0137-6934

Abstract

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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.

How to cite

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Zajączkowski, Wojciech. "$L_∞$-estimate for solutions of nonlinear parabolic systems." Banach Center Publications 33.1 (1996): 465-490. <http://eudml.org/doc/262704>.

@article{Zajączkowski1996,
abstract = {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.},
author = {Zajączkowski, Wojciech},
journal = {Banach Center Publications},
keywords = {-estimate; Steklov average; diagonal form},
language = {eng},
number = {1},
pages = {465-490},
title = {$L_∞$-estimate for solutions of nonlinear parabolic systems},
url = {http://eudml.org/doc/262704},
volume = {33},
year = {1996},
}

TY - JOUR
AU - Zajączkowski, Wojciech
TI - $L_∞$-estimate for solutions of nonlinear parabolic systems
JO - Banach Center Publications
PY - 1996
VL - 33
IS - 1
SP - 465
EP - 490
AB - 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.
LA - eng
KW - -estimate; Steklov average; diagonal form
UR - http://eudml.org/doc/262704
ER -

References

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  2. [2] J. P. Aubin and I. Ekeland, Applied Nonlinear Analysis, Wiley, New York, 1984. Zbl0641.47066
  3. [3] E. Di Benedetto, Degenerate Parabolic Eequations, Springer, 1993. 
  4. [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. Zbl0830.35053
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  6. [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. [7] O. A. Ladyzhenskaya and N. N. Uraltseva, Linear and Quasilinear Equations of Elliptic Type, Nauka, Moscow, 1973 (in Russian). 
  8. [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. Zbl0809.35134
  9. [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. Zbl0807.35074

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