Existence and uniqueness of a renormalized solution of parabolic problems in Orlicz spaces

Aberqi, Ahmed; Bennouna, Jaouad; Elmassoudi, Mhamed; Hammoumi, Mohamed

doi:10.1007/s00605-018-01260-8

Cited by 24 publications

(15 citation statements)

References 19 publications

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“…In this paper, we will be applying the Sobolev spaces with their variable exponents on the non-compact Riemannian manifolds theory to our equation (1). As for the structure of the paper, we will be sectioning it into: Recalling some definitions and Lemmas.…”

Section: Introductionmentioning

confidence: 99%

Existence and uniqueness of weak solution of p(x)- Laplacian in Sobolev spaces with variable exponents in complete manifolds

Benslimane

Aberqi

Bennouna

2021

Filomat

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Section: Introductionmentioning

confidence: 99%

Existence and uniqueness of weak solution of p(x)- Laplacian in Sobolev spaces with variable exponents in complete manifolds

Benslimane

Aberqi

Bennouna

2021

Filomat

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“…where f ∈ ðC 0 ðRÞÞ N and f ∈ L 1 (Ω). For more results, we refer the reader to [12][13][14][15][16][17][18][19][20][21][22][23][24] and references therein.…”

Section: Introductionmentioning

confidence: 99%

On some nonlinear anisotropic elliptic equations in anisotropic Orlicz space

Benslimane

Aberqi

Bennouna

2021

AJMS

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PurposeIn the present paper, the authors will discuss the solvability of a class of nonlinear anisotropic elliptic problems (P), with the presence of a lower-order term and a non-polynomial growth which does not satisfy any sign condition which is described by an N-uplet of N-functions satisfying the Δ2-condition, within the fulfilling of anisotropic Sobolev-Orlicz space. In addition, the resulting analysis requires the development of some new aspects of the theory in this field. The source term is merely integrable.Design/methodology/approachAn approximation procedure and some priori estimates are used to solve the problem.FindingsThe authors prove the existence of entropy solutions to unilateral problem in the framework of anisotropic Sobolev-Orlicz space with bounded domain. The resulting analysis requires the development of some new aspects of the theory in this field.Originality/valueTo the best of the authors’ knowledge, this is the first paper that investigates the existence of entropy solutions to unilateral problem in the framework of anisotropic Sobolev-Orlicz space with bounded domain.

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“…In Orlicz spaces we refer to [8] where L. Aharouch, J. Bennouna have proved the existence and uniqueness of entropy solutions in the framework of Orlicz Sobolev spaces W 1 0 L ϕ (Ω) assuming the △ 2 -condition on the Orlicz-function ϕ. Recently, the uniqueness of renormalized solution of (1) in the general case has been proven by A. Aberqi et al in [9] and by F. Kh. Mukminov in [10,11] for the Cauchy problem for anisotropic parabolic equation using Kruzhkov's method of doubling the variable.…”

Section: Introductionmentioning

confidence: 99%

Discrete solution for the nonlinear parabolic equations with diffusion terms in Museilak-spaces

Aberqi¹,

Elmassoudi²,

Hammoumi³

2021

Math. Model. Comput.

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In this paper, a class of nonlinear evolution equations with damping arising in fluid dynamics and rheology is studied. The nonlinear term is monotone and possesses a convex potential but exhibits non-standard growth. The appropriate functional framework for such equations is the modularly Museilak–spaces. The existence and uniqueness of a weak solution are proved using an approximation approach by combining an internal approximation with the backward Euler scheme, also a priori error estimate for the temporal semi-discretization is given.

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Existence and uniqueness of a renormalized solution of parabolic problems in Orlicz spaces

Cited by 24 publications

References 19 publications

Existence and uniqueness of weak solution of p(x)- Laplacian in Sobolev spaces with variable exponents in complete manifolds

Existence and uniqueness of weak solution of p(x)- Laplacian in Sobolev spaces with variable exponents in complete manifolds

On some nonlinear anisotropic elliptic equations in anisotropic Orlicz space

Discrete solution for the nonlinear parabolic equations with diffusion terms in Museilak-spaces

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