# ${L}_{\infty}$-estimate for solutions of nonlinear parabolic systems

Banach Center Publications (1996)

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

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topZajączkowski, 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

top- [1] H, W. Alt and S. Luckhaus, Quasilinear elliptic-parabolic differential equations, Math. Z. 183 (1983), 311-341. Zbl0497.35049
- [2] J. P. Aubin and I. Ekeland, Applied Nonlinear Analysis, Wiley, New York, 1984. Zbl0641.47066
- [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. Zbl0830.35053
- [5] J. Kacur, On a solution of degenerate elliptic-parabolic systems in Orlicz-Sobolev spaces I, Math. Z. 203 (1990), 153-171. Zbl0659.35045
- [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. Zbl0809.35134
- [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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