The Dirichlet Problem for Quasilinear Degenerate Parabolic Equations in One Dimension
- 数学科学－已发表论文 
考虑了一类一维拟线性退化抛物方程的Dirichlet问题,证明了其弱解存在性,主要思想是采用了压缩半群的方法,首先构造了一个耗散算子Ao,然后用正则化方法和椭圆方程理论.证明了方程u-λAou=v存在惟一解,结合指数公式,在L(?)上就可以构造压缩半群S(t)v.最后证明了由压缩半群构造的解S(t)uo满足方程．This paper is devoted to the study of the Dirichlet problem of quasilinear degenerate parabolic equations in one dimension, and by using the contraction semigroup method,the existence of the weak solution is obtained. First a dissipative operation Ao is constructed. Then by using the regularization method and the elliptic equations theory,the existence of the unique solution of the e-quation u-λAou=v is established. Employing exponential formula,a contraction semigroup S(t)v can be constructed in L(?). Finally it is proved that S(t)uo(x) is the weak solution.