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EXISTENCE RESULT FOR NONLINEAR PARABOLIC EQUATIONS WITH LOWER ORDER TERMS

Dipartimento di Matematica e Applicazioni "R. Caccioppoli", Università degli Studi di Napoli "Federico II", Complesso Monte S. Angelo, via Cintia, 80126 Napoli, Italy

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FILOMENA FEO

Dipartimento per le Tecnologie, Università degli Studi di Napoli Parthenope, Centro Direzionale Isola C4, 80100 Naples, Italy

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, and

OLIVIER GUIBÉ

Laboratoire de Mathématiques Raphaël Salem, Université de Rouen, CNRS, F-76801 Saint Etienne du Rouvray cedex, France

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https://doi.org/10.1142/S0219530511001790Cited by:26 (Source: Crossref)

Abstract

In this paper, we prove, the existence of a renormalized solution for a class of nonlinear parabolic problems whose prototype is

where Q_T = Ω × (0, T), Ω is an open and bounded subset of ℝ^N, N ≥ 2, T > 0, Δ_p is the so called p-Laplace operator,

, c ∈ (L^r(Q_T))^N with

, b ∈ L^{N+2, 1}(Q_T), f ∈ L¹(Q_T), g ∈ (L^p'(Q_T))^N and u₀ ∈ L¹(Ω).

Keywords:

AMSC: 35K55, 35K20, 35B45, 35R05

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