摘要
The authors study the singular diffusion equationwhere Ω(?)Rn is a bounded domain with appropriately smooth boundary δΩ, ρ(x) = dist(x,δΩ), and prove that if α≥p-1, the equation admits a unique solution subject only to a given initial datum without any boundary value condition, while if 0 <α< p - 1, for a given initial datum, the equation admits different solutions for different boundary value conditions.
基金
Project supported by the 973 Project of the Ministry of Science and Technology of China, the Outstanding Youth Foundation of China (No.10125107)
the Department of Mathematics of Jilin University.
