带有非强制项的非线性抛物问题的重整化解

Renormalized solutions for the nonlinear parabolic problem with lower order terms

通过逼近问题和截断函数,构造一个逼近序列,使其极限为问题的重整化解,即证明带有非强制性低阶项的非线性抛物问题的重整化解存在性,其右端项以及初始值均具有可积数据,这一问题区别于其他一般问题在于:方程左端项带有一个低阶项,其在Sobolev空间中没有强制性.

In the report,the approximate problem and truncation function were used to construct an approximate sequence,and whose limit was the renormalized solutions of the problem.The existence of renormalized solutions for the nonlinear and noncoercive parabolic problem with integrable data was proved.The problem was different from other general problems in that the left side of the equation has a lower order term,which is lack of coercivity in Sobolev space.