Existence of renormalized solutions for parabolic equations without the sign condition and with three unbounded nonlinearities

Y. Akdim, et al. "Existence of renormalized solutions for parabolic equations without the sign condition and with three unbounded nonlinearities." Applicationes Mathematicae 39.1 (2012): 1-22. <http://eudml.org/doc/280059>.

@article{Y2012,
abstract = {We study the problem ∂b(x,u)/∂t - div(a(x,t,u,Du)) + H(x,t,u,Du) = μ in Q = Ω×(0,T), $b(x,u)|_\{t=0\} = b(x,u₀)$ in Ω, u = 0 in ∂Ω × (0,T). The main contribution of our work is to prove the existence of a renormalized solution without the sign condition or the coercivity condition on H(x,t,u,Du). The critical growth condition on H is only with respect to Du and not with respect to u. The datum μ is assumed to be in $L¹(Q)+L^\{p^\{\prime \}\}(0,T;W^\{-1,p^\{\prime \}\}(Ω))$ and b(x,u₀) ∈ L¹(Ω).},
author = {Y. Akdim, J. Bennouna, M. Mekkour, H. Redwane},
journal = {Applicationes Mathematicae},
keywords = {truncations; time-regularization; coercivity condition; critical growth condition},
language = {eng},
number = {1},
pages = {1-22},
title = {Existence of renormalized solutions for parabolic equations without the sign condition and with three unbounded nonlinearities},
url = {http://eudml.org/doc/280059},
volume = {39},
year = {2012},
}

TY - JOUR
AU - Y. Akdim
AU - J. Bennouna
AU - M. Mekkour
AU - H. Redwane
TI - Existence of renormalized solutions for parabolic equations without the sign condition and with three unbounded nonlinearities
JO - Applicationes Mathematicae
PY - 2012
VL - 39
IS - 1
SP - 1
EP - 22
AB - We study the problem ∂b(x,u)/∂t - div(a(x,t,u,Du)) + H(x,t,u,Du) = μ in Q = Ω×(0,T), $b(x,u)|_{t=0} = b(x,u₀)$ in Ω, u = 0 in ∂Ω × (0,T). The main contribution of our work is to prove the existence of a renormalized solution without the sign condition or the coercivity condition on H(x,t,u,Du). The critical growth condition on H is only with respect to Du and not with respect to u. The datum μ is assumed to be in $L¹(Q)+L^{p^{\prime }}(0,T;W^{-1,p^{\prime }}(Ω))$ and b(x,u₀) ∈ L¹(Ω).
LA - eng
KW - truncations; time-regularization; coercivity condition; critical growth condition
UR - http://eudml.org/doc/280059
ER -