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

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Akdim Y., Bennouna J., Mekkour M., Redwane H.

Applicationes Mathematicae

2012

tom 39

nr 1

1-22

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 $L¹(Q)+L^{p'}(0,T;W^{-1,p'}(Ω))$ and b(x,u₀) ∈ L¹(Ω).

Ograniczanie wyników

1 Applicationes Mathematicae

1 Akdim Y.

1 Bennouna J.

1 Mekkour M.

1 Redwane H.

1 2012

Wyniki wyszukiwania

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