The Dirichlet Problem for Quasilinear Degenerate Parabolic Equations in One Dimension
QU Cheng-yuan · Journal of Xiamen University · 2006
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.