Existence of renormalized solutions for parabolic equations without the sign condition and with three unbounded nonlinearities
Y. Akdim ; J. Bennouna ; M. Mekkour ; H. Redwane
Applicationes Mathematicae, Tome 39 (2012), p. 1-22 / Harvested from The Polish Digital Mathematics Library
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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)+Lp'(0,T;W-1,p'(Ω)) and b(x,u₀) ∈ L¹(Ω).

Publié le : 2012-01-01
EUDML-ID : urn:eudml:doc:280059 
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     author = {Y. Akdim and J. Bennouna and M. Mekkour and H. Redwane},
     title = {Existence of renormalized solutions for parabolic equations without the sign condition and with three unbounded nonlinearities},
     journal = {Applicationes Mathematicae},
     volume = {39},
     year = {2012},
     pages = {1-22},
     zbl = {1242.35151},
     language = {en},
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Y. Akdim; J. Bennouna; M. Mekkour; H. Redwane. Existence of renormalized solutions for parabolic equations without the sign condition and with three unbounded nonlinearities. Applicationes Mathematicae, Tome 39 (2012) pp. 1-22. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am39-1-1/