Existence of periodic solutions for some quasilinear parabolic problems with variable exponents

Hachimi, Abderrahmane El; Maatouk, Soufiane

doi:10.1007/s40065-017-0178-0

Cited by 3 publications

(2 citation statements)

References 17 publications

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“…Thus ∇u 1 = ∇u 2 in (L p(•) ( )) 9 , and by the inequality of Poincaré, we get u 1 = u 2 in (L p(•) ( )) 3 , and so u 1 = u 2 dans (W 1,p(•) ( )) 3 .…”

Section: Abbreviationsmentioning

confidence: 86%

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On a nonlinear elasticity problem with friction and Sobolev spaces with variable exponents

Boukrouche

Merouani

Fayrouz

2022

Fixed Point Theory Algorithms Sci Eng

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We consider a nonlinear elasticity problem in a bounded domain, its boundary is decomposed in three parts: lower, upper, and lateral. The displacement of the substance, which is the unknown of the problem, is assumed to satisfy the homogeneous Dirichlet boundary conditions on the upper part, and not homogeneous one on the lateral part, while on the lower part, friction conditions are considered. In addition, the problem is governed by a particular constitutive law of elasticity system with a strongly nonlinear strain tensor. The functional framework leads to using Sobolev spaces with variable exponents. The formulation of the problem leads to a variational inequality, for which we prove the existence and uniqueness of the solution of the associated variational problem.

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“…Thus ∇u 1 = ∇u 2 in (L p(•) ( )) 9 , and by the inequality of Poincaré, we get u 1 = u 2 in (L p(•) ( )) 3 , and so u 1 = u 2 dans (W 1,p(•) ( )) 3 .…”

Section: Abbreviationsmentioning

confidence: 86%

“…2, we recall some definitions and properties of Lebesgue and Sobolev spaces with variable exponents (see for example [5-7, 10, 11] for the proofs and more details). This notion of Sobolev spaces with variable exponents is also used in many works (see for example [1,9,14]).…”

Section: Introductionmentioning

confidence: 99%