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

Ahmed Aberqi, et al. "Existence results for a class of nonlinear parabolic equations with two lower order terms." Applicationes Mathematicae 41.2-3 (2014): 207-219. <http://eudml.org/doc/279941>.

@article{AhmedAberqi2014,
abstract = {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).},
author = {Ahmed Aberqi, Jaouad Bennouna, M. Hammoumi, Mounir Mekkour, Ahmed Youssfi},
journal = {Applicationes Mathematicae},
keywords = {Sobolev space; renormalized solutions; nonlinear parabolic equations},
language = {eng},
number = {2-3},
pages = {207-219},
title = {Existence results for a class of nonlinear parabolic equations with two lower order terms},
url = {http://eudml.org/doc/279941},
volume = {41},
year = {2014},
}

TY - JOUR
AU - Ahmed Aberqi
AU - Jaouad Bennouna
AU - M. Hammoumi
AU - Mounir Mekkour
AU - Ahmed Youssfi
TI - Existence results for a class of nonlinear parabolic equations with two lower order terms
JO - Applicationes Mathematicae
PY - 2014
VL - 41
IS - 2-3
SP - 207
EP - 219
AB - 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).
LA - eng
KW - Sobolev space; renormalized solutions; nonlinear parabolic equations
UR - http://eudml.org/doc/279941
ER -