Nonlinear parabolic inequalities with lower order terms

Obstacle parabolic equations in non-reflexive Musielak-Orlicz spaces

“…Starting with the paper [8] where g = 0, the existence results have been proved in the framework of Classical Sobolev spaces in ( [5], [7], [15]) where g(x, t, u) = g(u) continuous function on u in the Orlicz spaces. For the lower order g = 0 depending on x, t and u and without coercivity condition, the problem (1.1) was treated firstly in [14] and recently in ( [1]), [2], [9]) using the framework of renormalized solutions. In Musielak spaces Gwiazda et al in [11], have been proved the renormalized solution where the conjugate of Musielak-Orlicz function satisfies the ∆ 2 -condition and in [12] where b(x, u) = u and g = 0.…”

“…In Musielak spaces Gwiazda et al in [11], have been proved the renormalized solution where the conjugate of Musielak-Orlicz function satisfies the ∆ 2 -condition and in [12] where b(x, u) = u and g = 0. The aim of this paper is to generalize [1,11,12] and reducing the hypotheses either for the lower nonlinear term g and the framework, i.e. the inhomogeneous space W 1,x L M (Q T ) without 2 -condition on M and M, which introduces some complexity understanding if the dual pairing.…”

A few results on some nonlinear parabolic problems in Orlicz-Sobolev spaces

“…In this paper, we survey some existence results for a class of parabolic problems, we refer to [1,2,19] for an extended treatment. Let Ω be a bounded open subset of R N , N ≥ 2, Q = Ω × (0, T) where T is a positive real number and M is an Orlicz function.…”

Nonlinear parabolic problem with lower order terms in Musielak-Orlicz spaces

“…To our knowledge, differential equations in general MusielakSobolev spaces have been studied rarely see [10][11][12][13][14], then our aim in this paper is to overcome some difficulties encountered in these spaces and to generalize the result of [4,9,15,16], and we prove an existence result of entropy solution for the obstacle parabolic problem (1), with less restrictive growth, and no coercivity condition in the first lower order term Φ, and without sign condition in the second lower order H, in the framework of inhomogeneous Orlicz-Sobolev spaces W 1,x 0 L M (Q T ), and N-function M, defining space does not satisfy the 2 -condition. This paper is organized as follows.…”

“…∈ L 2 (Q T ) and p = 2, in [2] have proved the existence of entropy solutions, recently in [3] have proved an existence results of renormalized solutions in the case where p ≥ 2 and c(., .) ∈ L r (Q T ) with r > N +p p−1 , and by in [4] for more general parabolic term. For the elliptic version of the problem (1), more results are obtained see e.g.…”