Existence and uniqueness result for a class of nonlinear parabolic equations with L¹ data
We prove the existence and uniqueness of a renormalized solution for a class of nonlinear parabolic equations with no growth assumption on the nonlinearities.
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Kaouther Ammar, Jaouad Bennouna, Hicham Redwane (2014)
Applicationes Mathematicae
We prove the existence and uniqueness of a renormalized solution for a class of nonlinear parabolic equations with no growth assumption on the nonlinearities.
Y. Akdim, J. Bennouna, M. Mekkour, H. Redwane (2012)
Applicationes Mathematicae
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), 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 and b(x,u₀) ∈ L¹(Ω).
Ahmed Aberqi, Jaouad Bennouna, Hicham Redwane (2014)
Applicationes Mathematicae
We prove the existence of a renormalized solution to a class of doubly nonlinear parabolic systems.
Abderrahmane El Hachimi, Jaouad Igbida, Ahmed Jamea (2010)
Applicationes Mathematicae
We study the existence of solutions of the nonlinear parabolic problem in ]0,T[ × Ω, on ]0,T[ × ∂Ω, u(0,·) = u₀ in Ω, with initial data in L¹. We use a time discretization of the continuous problem by the Euler forward scheme.
Ahmed Aberqi, Jaouad Bennouna, M. Hammoumi, Mounir Mekkour, Ahmed Youssfi (2014)
Applicationes Mathematicae
We investigate the existence of renormalized solutions for some nonlinear parabolic problems associated to equations of the form ⎧ in Q = Ω×(0,T), ⎨ u(x,t) = 0 on ∂Ω ×(0,T), ⎩ in Ω. with s = (N+2)/(N+p) (p-1), , τ = (N+p)/(p-1), r = (N(p-1) + p)/(N+2), and f ∈ L¹(Q).
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