Geodesic
Existence of a renormalized solutions to a nonlinear system in Orlicz spaces
Filomat, Tome 36 (2022) no. 15, p. 5073

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DOI

In this paper, we will be concerned with the existence of renormalized solutions to the following parabolic-elliptic system ∂u ∂t + Au = σ(u)|∇φ|2 in QT = Ω × (0,T), −div(σ(u)∇φ) = divF(u) in QT, u = 0 on ∂Ω × (0,T), φ = 0 on ∂Ω × (0,T), u(·, 0) = u0 in Ω, where Au = −div a(x, t,u,∇u) is a Leray-Lions operator defined on the inhomogeneous Orlicz-Sobolev space W1,x0 LM(QT) into its dual, M is a N-function related to the growth of a. M does not satisfy the ∆2-condition, and σ and F are two Carathéodory functions defined in QT ×R.
DOI : 10.2298/FIL2215073A
Classification : 35M10, 35J60, 35K65
Keywords: Renormalized solutions, nonlinear elliptic equations, nonlinear parabolic equations, weak solutions, Orlicz-Sobolev spaces 
Yassine Ahakkouda; Jaouad Bennounaa; Mhamed Elmassoudia. Existence of a renormalized solutions to a nonlinear system in Orlicz spaces. Filomat, Tome 36 (2022) no. 15, p. 5073 . doi: 10.2298/FIL2215073A
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     author = {Yassine Ahakkouda and Jaouad Bennounaa and Mhamed Elmassoudia},
     title = {Existence of a renormalized solutions to a nonlinear system in {Orlicz} spaces},
     journal = {Filomat},
     pages = {5073 },
     year = {2022},
     volume = {36},
     number = {15},
     doi = {10.2298/FIL2215073A},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2215073A/}
}
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