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Renormalized Solutions of Nonlinear Degenerated Parabolic Equations Without Sign Condition and L1 Data $45.00
Authors:  Youssef Akdim, Jaouad Bennouna and Mounir Mekkour
Abstract:
In this paper, we study the problem:

∂u/∂t - div (a(x, t, u,Du))+ H(x, t, u,Du) = f in ΩX]0,T[,
u(x,0) = u0 in Ω
u = 0 in ∂ΩX]0,T[

in the framework of weighted Sobolev space. The main contribution of our work is to prove the existence of a renormalized solution without the sign condition and the coercivity condition on H(x, t, u, Du), the critical growth condition on H is with respect to Du and no growth with respect to u. The second term f belongs to L1(Q) and u0 ε L1(Ω). 


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Renormalized Solutions of Nonlinear Degenerated Parabolic Equations Without Sign Condition and L<sup>1</sup> Data