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Abstrakty
We investigate the existence of renormalized solutions for some nonlinear parabolic problems associated to equations of the form
⎧$∂(e^{βu}-1)/∂t - div(|∇u|^{p-2}∇u) + div(c(x,t)|u|^{s-1}u) + b(x,t)|∇u|^{r} = f$ in Q = Ω×(0,T),
⎨ u(x,t) = 0 on ∂Ω ×(0,T),
⎩ $(e^{βu} - 1)(x,0) = (e^{βu₀} - 1)(x)$ in Ω.
with s = (N+2)/(N+p) (p-1), $c(x,t) ∈ (L^{τ}(QT))^{N}$, τ = (N+p)/(p-1), r = (N(p-1) + p)/(N+2), $b(x,t) ∈ L^{N+2,1}(QT)$ and f ∈ L¹(Q).
⎧$∂(e^{βu}-1)/∂t - div(|∇u|^{p-2}∇u) + div(c(x,t)|u|^{s-1}u) + b(x,t)|∇u|^{r} = f$ in Q = Ω×(0,T),
⎨ u(x,t) = 0 on ∂Ω ×(0,T),
⎩ $(e^{βu} - 1)(x,0) = (e^{βu₀} - 1)(x)$ in Ω.
with s = (N+2)/(N+p) (p-1), $c(x,t) ∈ (L^{τ}(QT))^{N}$, τ = (N+p)/(p-1), r = (N(p-1) + p)/(N+2), $b(x,t) ∈ L^{N+2,1}(QT)$ and f ∈ L¹(Q).
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
207-219
Opis fizyczny
Daty
wydano
2014
Twórcy
autor
- Laboratory LAMA, Department of Mathematics, Faculty of Sciences Dhar El Mahraz, Sidi Mohamed Ben Abdellah University, P.O. Box 1796 Atlas, Fez, Morocco
autor
- Laboratory LAMA, Department of Mathematics, Faculty of Sciences Dhar El Mahraz, Sidi Mohamed Ben Abdellah University, P.O. Box 1796 Atlas, Fez, Morocco
autor
- Laboratory LAMA, Department of Mathematics, Faculty of Sciences Dhar El Mahraz, Sidi Mohamed Ben Abdellah University, P.O. Box 1796 Atlas, Fez, Morocco
autor
- Laboratory LIMAO, Poly-disciplinary Faculty of Taza, Sidi Mohamed Ben Abdellah University, P.O. Box 1223, Taza, Morocco
autor
- Deptment of Mathematics, Faculty of Sciences and Technology, Moulay Ismail University, P.O. Box 509-Boutalamine, 52 000 Errachidia, Morocco
Bibliografia
Typ dokumentu
Bibliografia
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DOI
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-am41-2-8