Nonnegative weak solution for a periodic parabolic equation with bounded Radon measure

Charkaoui, Abderrahim; Alaa, Nour Eddine

doi:10.1007/s12215-021-00614-w

Cited by 10 publications

(3 citation statements)

References 18 publications

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“…Among the novelty of our work, we establish an interesting compactness result which will be applied in the studies of periodic parabolic systems with nonstandard growth conditions. As can be viewed the results of our paper generalized the existing work in the literature not only on the constant exponent case 2,3,4,11,13,14,15,18 but also these involving variable exponent with particular assumptions on the nonlinearities 7,12,21,35,38 .…”

Section: Introductionsupporting

confidence: 54%

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Time periodic solutions for strongly nonlinear parabolic systems with p(x)-growth conditions

CHARKAOUI,

Alaa,

Alaa

2024

Preprint

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We study a class of nonlinear periodic systems driven by general differential operators with variable exponent. We assume that the reactions contains p(x)-growth nonlinearities with respect to the gradients. By using Leray Schauder’s topological degree combined with the sub- and super-solutions method, we establish the existence and uniqueness results of weak periodic solutions to the studied systems.

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Section: Introductionsupporting

confidence: 54%

“…At the same time, the literature of periodic PDEs is very vast and for more clarification, we refer the readers to see the works 6,11,13,14,15,16,20,25 . Particularly, in 6 Amann studied a periodic parabolic equation with an additionnal nonlinearity and subquadratic growth on the gradient.…”

Section: Introductionmentioning

confidence: 99%

Time periodic solutions for strongly nonlinear parabolic systems with p(x)-growth conditions

CHARKAOUI,

Alaa,

Alaa

2024

Preprint

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“…A large literature exists on periodic equations and several researchers have been interested in the subject, we quote in particular [8,6,11,12,13,15,14,18,19,23,24]. We start by referring the readers to see the book [24] for a major and comprehensive introduction to periodic parabolic equations with regular data.…”

Section: Introductionmentioning

confidence: 99%

Periodic parabolic problem with discontinuous coefficients: Mathematical analysis and numerical simulation

Alaa

Charkaoui²,

Elaassri³

2022

Proyecciones (Antofagasta)

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This work presents a new approach for the mathematical analysis and numerical simulation of a class of periodic parabolic equations with discontinuous coefficients. Our technique is based on the minimization of a least squares cost function. By the means of variational calculus, we prove that the considered optimization problem admits an optimal solution. Using the Lagrangian method, we compute the gradient of the cost function associated with our problem. Finally, we give several numerical simulations that show the efficiency and robustness of our method.

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An $$L^1$$-theory for a nonlinear temporal periodic problem involving p(x)-growth structure with a strong dependence on gradients

Charkaoui,

Alaa

2023

J. Evol. Equ.

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Nonnegative weak solution for a periodic parabolic equation with bounded Radon measure

Cited by 10 publications

References 18 publications

Time periodic solutions for strongly nonlinear parabolic systems with p(x)-growth conditions

Time periodic solutions for strongly nonlinear parabolic systems with p(x)-growth conditions

Periodic parabolic problem with discontinuous coefficients: Mathematical analysis and numerical simulation

An $$L^1$$-theory for a nonlinear temporal periodic problem involving p(x)-growth structure with a strong dependence on gradients

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