Renormalized Solutions for Nonlinear Parabolic Systems with Three Unbounded Nonlinearities in Weighted Sobolev Spaces

Renormalized Solutions for Nonlinear Parabolic Systems with Three Unbounded Nonlinearities in Weighted Sobolev Spaces

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摘要 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 { b1（x,u1）/ t-div（a（x,t,u1,Du1））＋div（Ф1（u1））＋f1（x,u1,u2）=O in Q, b2（x,u2）/ t-div（a（x,t,u2,Du2））＋div（Ф2（u2））＋f2（x,u1,u2）=O in Q in the framework of weighted Sobolev spaces, where b（x,u） is unbounded function on u, the Carath6odory function ai satisfying the coercivity condition, the general growth condition and only the large monotonicity, the function Фi is assumed to be continuous on ]R and not belong to （Lloc1（Q））N. 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 { b1（x,u1）/ t-div（a（x,t,u1,Du1））＋div（Ф1（u1））＋f1（x,u1,u2）=O in Q, b2（x,u2）/ t-div（a（x,t,u2,Du2））＋div（Ф2（u2））＋f2（x,u1,u2）=O in Q in the framework of weighted Sobolev spaces, where b（x,u） is unbounded function on u, the Carath6odory function ai satisfying the coercivity condition, the general growth condition and only the large monotonicity, the function Фi is assumed to be continuous on ]R and not belong to （Lloc1（Q））N.

作者 Y. Akdim J. Bennouna A. Bouajaja M.Mekkour

机构地区 UniversitSidi Mohamed Ben Abdellah UniversitSidi Mohamed Ben Abdellah

出处《Analysis in Theory and Applications》 2013年第3期234-254,共21页 分析理论与应用（英文刊）

关键词 Nonlinear parabolic system EXISTENCE TRUNCATION weighted Sobolev space renor-malized solution. Nonlinear parabolic system, existence, truncation, weighted Sobolev space, renor-malized solution.

分类号 O175.26 [理学—基础数学]

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Renormalized Solutions for Nonlinear Parabolic Systems with Three Unbounded Nonlinearities in Weighted Sobolev Spaces

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