@Article{ATA-29-234,
author = {Y. Akdim , J. Bennouna , Bouajaja , A. and Mekkour , M.},
title = {Renormalized Solutions for Nonlinear Parabolic Systems with Three Unbounded Nonlinearities in Weighted Sobolev Spaces},
journal = {Analysis in Theory and Applications},
year = {2013},
volume = {29},
number = {3},
pages = {234--254},
abstract = {<p style="text-align: justify;">We prove an existence result without assumptions on the growth of some nonlinear terms, and the existence of a renormalized solution. In this work, we study the existence of renormalized solutions for a class of nonlinear parabolic systems with three unbounded nonlinearities, in the form$$ \left\{\begin{array}{ll} \dfrac{\partial b_1(x,u_1)}{\partial t}- \mathop{div}\big(a(x,t,u_1,Du_1)\big)+\mathop{div}\big(\Phi_1(u_1)\big)+ f_1(x,u_1,u_2)= 0 &nbsp;&amp; &nbsp;\quad\text{in}\ \ &nbsp;Q, \\\dfrac{\partial b_2(x,u_2)}{\partial t}- \mathop{div}\big(a(x,t,u_2,Du_2)\big)+\mathop{div}\big(\Phi_2(u_2)\big)+ f_2(x,u_1,u_2)= 0 &nbsp;&amp; \quad\text{in}\ \ &nbsp;Q, \\\end{array}\right.$$in the framework of weighted Sobolev spaces, where $b(x,u)$ is unbounded function on $u$, the Carathéodory function $a_i$ satisfying the coercivity condition, the general growth condition and only the large monotonicity, the function $\phi_i$ is assumed to be continuous on $\mathbb{R}$ and not belong to $(L^1_{loc}(Q))^N$.</p>},
issn = {1573-8175},
doi = {https://doi.org/10.4208/ata.2013.v29.n3.4},
url = {http://global-sci.org/intro/article_detail/ata/5060.html}
}