Existence results for a class of nonlinear parabolic equations with two lower order terms

Ahmed Aberqi; Jaouad Bennouna; M. Hammoumi; Mounir Mekkour; Ahmed Youssfi

Ahmed Aberqi ; Jaouad Bennouna ; M. Hammoumi ; Mounir Mekkour ; Ahmed Youssfi

Applicationes Mathematicae, Tome 41 (2014), p. 207-219 / Harvested from The Polish Digital Mathematics Library

Résumé

We investigate the existence of renormalized solutions for some nonlinear parabolic problems associated to equations of the form ⎧ $\partial (e^{β u} - 1) / \partial t - {d i v (| \nabla u |}^{p - 2} \nabla u) + d i v (c (x, t) {| u |}^{s - 1} u) + b (x, t) {| \nabla u |}^{r} = f$ in Q = Ω×(0,T), ⎨ u(x,t) = 0 on ∂Ω ×(0,T), ⎩ $(e^{β u} - 1) (x, 0) = (e^{β u ₀} - 1) (x)$ in Ω. with s = (N+2)/(N+p) (p-1), $c (x, t) \in {(L^{τ} (Q T))}^{N}$ , τ = (N+p)/(p-1), r = (N(p-1) + p)/(N+2), $b (x, t) \in L^{N + 2, 1} (Q T)$ and f ∈ L¹(Q).

Publié le : 2014-01-01

Zbl 1327.35202

EUDML-ID : urn:eudml:doc:279941

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     author = {Ahmed Aberqi and Jaouad Bennouna and M. Hammoumi and Mounir Mekkour and Ahmed Youssfi},
     title = {Existence results for a class of nonlinear parabolic equations with two lower order terms},
     journal = {Applicationes Mathematicae},
     volume = {41},
     year = {2014},
     pages = {207-219},
     zbl = {1327.35202},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am41-2-8}
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Ahmed Aberqi; Jaouad Bennouna; M. Hammoumi; Mounir Mekkour; Ahmed Youssfi. Existence results for a class of nonlinear parabolic equations with two lower order terms. Applicationes Mathematicae, Tome 41 (2014) pp. 207-219. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am41-2-8/