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

• Autorzy: Wojciech M. Zajączkowski
• Języki publikacji: EN

Abstrakty

EN

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.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 1996
• Tom: 33
• Numer: 1
• Strony: 491-501

Daty

wydano

1996

Twórcy

autor

Wojciech M. Zajączkowski

• Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-950 Warszawa, Poland

Bibliografia

• [1] H. W. Alt and S. Luckhaus, Quasilinear elliptic-parabolic differential equations, Math. Z. 183 (1983) 311-341.
• [2] J. P. Aubin and I. Ekeland, Applied Nonlinear Analysis, Wiley, New York, 1984.
• [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).
• [6] M. Wiegner, Global solutions to a class of strongly coupled parabolic systems, Math. Ann. 292 (1992), 711-727.
• [7] W. M. Zajączkowski, $L_∞$-estimate for solutions of nonlinear parabolic systems, this volume.