Some properties of Musielak spaces with only the log-Hölder continuity condition and application

Khellou, Mustafa Ait; Benkirane, Abdelmoujib; Douiri, Sidi Mohamed

doi:10.1007/s43034-020-00069-7

Cited by 16 publications

(15 citation statements)

References 16 publications

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“…, the a priori estimate in (15) proves the weak convergence of a subsequence of { u ℓ (•, T )} in L 2 (Ω) and also its limit can be written as b(z) where z ∈ L 2 (Ω).…”

Section: Convergence Of the Numerical Solution (U ℓ )mentioning

confidence: 94%

“…584-600 (2021)for any 0 < ε < 1. From where we have(15). For the second inequality using only (2) to get b 0 |u n − u n−1 | |b(u n ) − b(u n−1 )| and by(15), we deduce(16).…”

mentioning

confidence: 87%

“…It is a separable space and (E ϕ (Ω)) * = L ϕ (Ω) [15]. E ϕ (Ω) = K ϕ (Ω) if and only if ϕ satisfies the ∆ 2 -condition for the large values of t or for all values of t, according to whether Ω has finite measure or not.…”

Section: Musielak Spacementioning

confidence: 99%

“…Lemma 1 (Ref. [15]). (Approximation result) Ω be a bounded Lipschitz domain in R d and let ϕ and ϕ be two complementary Musielak functions satisfying the following conditions:…”

Section: Musielak Spacementioning

confidence: 99%

“…and the inequality (15) shows the boundedness of {b(u ℓ )} and { u ℓ } in L ∞ (0, T ; L 2 (Ω)). Thus weak* convergence of a subsequence in L ∞ (0, T ; L 2 (Ω)) is stated.…”

Section: Convergence Of the Numerical Solution (U ℓ )mentioning

confidence: 99%

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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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“…, the a priori estimate in (15) proves the weak convergence of a subsequence of { u ℓ (•, T )} in L 2 (Ω) and also its limit can be written as b(z) where z ∈ L 2 (Ω).…”

Section: Convergence Of the Numerical Solution (U ℓ )mentioning

confidence: 94%

“…584-600 (2021)for any 0 < ε < 1. From where we have(15). For the second inequality using only (2) to get b 0 |u n − u n−1 | |b(u n ) − b(u n−1 )| and by(15), we deduce(16).…”

mentioning

confidence: 87%

Section: Musielak Spacementioning

confidence: 99%

“…Lemma 1 (Ref. [15]). (Approximation result) Ω be a bounded Lipschitz domain in R d and let ϕ and ϕ be two complementary Musielak functions satisfying the following conditions:…”

Section: Musielak Spacementioning

confidence: 99%

“…and the inequality (15) shows the boundedness of {b(u ℓ )} and { u ℓ } in L ∞ (0, T ; L 2 (Ω)). Thus weak* convergence of a subsequence in L ∞ (0, T ; L 2 (Ω)) is stated.…”

Section: Convergence Of the Numerical Solution (U ℓ )mentioning

confidence: 99%

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