L ∞ -estimates for solutions of nonlinear parabolic systems with gradient linear growth

Wojciech Zajączkowski

Banach Center Publications (1996)

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

Abstract

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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.

How to cite

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Zajączkowski, 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

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  1. [1] H. W. Alt and S. Luckhaus, Quasilinear elliptic-parabolic differential equations, Math. Z. 183 (1983) 311-341. Zbl0497.35049
  2. [2] J. P. Aubin and I. Ekeland, Applied Nonlinear Analysis, Wiley, New York, 1984. Zbl0641.47066
  3. [3] E. DiBenedetto, Degenerate Parabolic Equations, Springer, 1993. 
  4. [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. [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. [6] M. Wiegner, Global solutions to a class of strongly coupled parabolic systems, Math. Ann. 292 (1992), 711-727. Zbl0801.35064
  7. [7] W. M. Zajączkowski, L ∞ -estimate for solutions of nonlinear parabolic systems, this volume. 

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