Existence Result for Nonlinear Parabolic Equations With Lower Order Terms

Abstract

In this paper, we prove, the existence of a renormalized solution for a class of nonlinear parabolic problems whose prototype is [Formula: see text] where QT = Ω × (0, T), Ω is an open and bounded subset of ℝN, N ≥ 2, T > 0, Δp is the so called p-Laplace operator, [Formula: see text], c ∈ (Lr(QT))N with [Formula: see text], [Formula: see text], b ∈ LN+2, 1(QT), f ∈ L1(QT), g ∈ (Lp'(QT))N and u0 ∈ L1(Ω).

Doubly Nonlinear Parabolic Systems In Inhomogeneous Musielak- Orlicz-Sobolev Spcaes

“…One of the models of applications of these operators is the system of Boussinesq: (∇u + (∇u) t ) is the strain rate tensor. It is our purpose, in this paper to generalize the result of ( [1], [2], [3]) and we prove the existence of a renormalized solution of system (1.1).…”

Renormalized Solution for a nonlinear parabolic problems with noncoercivity in divergence form in Orlicz Spaces

“…In some works of Guibé, specially when he treated certain non-coercive problems, in general the term ÀdivðcðxÞjuj c Þ or ÀdivðUðx; uÞÞ produces a lack of coercivity of operator, to handle this term Guibé and Ben Cheikh Ali (See [14]) assume the following growth condition jUðx; uÞj 6 bðxÞð1 þ juj pÀ1 Þ and Di Nardo et al in [13] assume that jUðx; uÞj 6 cðxÞjuj c where c 6 p À 1 in the classical Sobolev Spaces.…”

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

“…For c(., .) ∈ 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.…”