J. Nonl. Evol. Equ. Appl. 2014 (7), pp. 101-130, published on February 23, 2015:

Entropy solutions of nonlinear parabolic equations in Orlicz-Sobolev spaces, without sign condition and L¹ data

University of Fez, Faculty of Sciences Dhar El Mahraz, Laboratory LAMA, Department of Mathematics, B.P 1796 Atlas Fez, Morocco

Faculty of Juridical, Economic and Social Sciences, Hassan 1 University, B.P 784, Settat, Morocco.

University of Fez, Faculty of Sciences Dhar El Mahraz, Laboratory LAMA, Department of Mathematics, B.P 1796 Atlas Fez, Morocco

Received on February 24, 2013
Accepted on June 3, 2013

Communicated by A. Pankov

Abstract. We give an existence result of the obstacle parabolic associated to the problemb_t(u) − div a(x; t; u; Du) + g(x; t; u; Du) = f in Ω × (0; T), where b(u) is an unbounded function and where −div(a(x; t; u; Du)) is a Leray-Lions operator in Orlicz-Sobolev spaces. The critical growth condition on g is with respect to Du, no growth with respect to u and without the sign condition. The R.H.S. f belongs to L¹(Ω × (0; T)) and u₀ ∈ L¹(Ω).
Keywords:	Nonlinear parabolic unilateral. Entropy solutions. Orlicz Sobolev spaces. Sign condition.
2010 Mathematics Subject Classification: Primary 47A15; Secondary 46A32, 47D20.