摘要
We establish the existence of continuous solutions of the first boundary value prob- lem for nonlinar diffusion equations of the form θu/ t=div(α（u）|▽u|<sup>m-1</sup>▽u)+ （u）▽u, under the conditions that A（s）=integral from n=o to s(a<sup>1/m</sup>（σ）dσis strictly increasing and m】n-1,where n is the space dimension.Moreover,the uniqueness is proved for solutions with some regularities.
We establish the existence of continuous solutions of the first boundary value prob- lem for nonlinar diffusion equations of the form θu/ t=div(α（u）|▽u|<sup>m-1</sup>▽u)+ （u）▽u, under the conditions that A（s）=integral from n=o to s(a<sup>1/m</sup>（σ）dσis strictly increasing and m>n-1,where n is the space dimension.Moreover,the uniqueness is proved for solutions with some regularities.
基金
National Natural Science Foundation of China.
