四阶抛物型方程在加权空间下临界状态的小初值问题

The Small Initial Value Problem for the Four Order Parabolic Equation under the Weighted Space Condition

研究了一类四阶抛物型方程在加权的L^P空间下的小初值问题.应用Sobolev嵌入定理、Fourier分解和象征算子及压缩映射等方法,证明出了此类四阶抛物型方程在临界状态σ=4/n时,小初值解的存在唯一性和最优衰减估计,从而为图像处理奠定了理论基础.

In this paper,we study a small initial value problem for a class of four order parabolic equation in weighted space of L^p.By means of Sobolev embedding theorem,Fourier Transform and symbolic operator and compression mapping,the existence and uniqueness of the small initial value solution and the optimal decay estimate for the four order parabolic equation in the critical state of σ=4/n are proved.