二阶拟线性退化抛物方程Cauchy问题弱解的存在性

摘要

对于拟线性退化抛物方程,很多学者已经对其Cauchy问题的粘性解进行了讨论,但如果考虑的是弱解,将会有不同的处理方法,文章对一类二阶拟线性退化抛物方程的Cauchy问题进行了研究,利用压缩半群理论,证明了其弱解的存在性。%For a quasilinear degenerate parabolic equation, many scholars have discussed its Viscosity solution of the Cauchy problem, but if considerating the weak solution,it will have a different treatment method. This article does some research summary on the Cauchy problem of a second order quasilinear degenerate parabolic equation, and proves the existence of the weak solution of the Cauchy prob- lem by using the contraction semigroup theory.