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

top
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

top

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

top
  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. 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
  5. [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. [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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.