# ${L}_{\infty}$-estimates for solutions of nonlinear parabolic systems with gradient linear growth

Banach Center Publications (1996)

- Volume: 33, Issue: 1, page 491-501
- ISSN: 0137-6934

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topZajączkowski, Wojciech. "$L_∞$-estimates for solutions of nonlinear parabolic systems with gradient linear growth." Banach Center Publications 33.1 (1996): 491-501. <http://eudml.org/doc/262758>.

@article{Zajączkowski1996,

abstract = {Existence of weak solutions and an $L_∞$-estimate are shown for nonlinear nondegenerate parabolic systems with linear growth conditions with respect to the gradient. The $L_∞$-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.},

author = {Zajączkowski, Wojciech},

journal = {Banach Center Publications},

keywords = {gradient linear growth},

language = {eng},

number = {1},

pages = {491-501},

title = {$L_∞$-estimates for solutions of nonlinear parabolic systems with gradient linear growth},

url = {http://eudml.org/doc/262758},

volume = {33},

year = {1996},

}

TY - JOUR

AU - Zajączkowski, Wojciech

TI - $L_∞$-estimates for solutions of nonlinear parabolic systems with gradient linear growth

JO - Banach Center Publications

PY - 1996

VL - 33

IS - 1

SP - 491

EP - 501

AB - Existence of weak solutions and an $L_∞$-estimate are shown for nonlinear nondegenerate parabolic systems with linear growth conditions with respect to the gradient. The $L_∞$-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.

LA - eng

KW - gradient linear growth

UR - http://eudml.org/doc/262758

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. DiBenedetto, Degenerate Parabolic Equations, Springer, 1993.
- [4] O. A. Ladyzhenskaya, V. A. Solonnikov and N. N. Uraltseva, Linear and Quasilinear Equations of Parabolic Type, Amer. Math. Soc., Providence, R.I., 1968.
- [5] V. A. Solonnikov, On boundary problems for linear parabolic systems of differential equations of general type, Trudy Mat. Inst. Steklov. 83 (1965) (in Russian); English transl.: Proc. Steklov Inst. Math. 83 (1967). Zbl0164.12502
- [6] M. Wiegner, Global solutions to a class of strongly coupled parabolic systems, Math. Ann. 292 (1992), 711-727. Zbl0801.35064
- [7] W. M. Zajączkowski, ${L}_{\infty}$-estimate for solutions of nonlinear parabolic systems, this volume.

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