中文摘要：

主要考虑一类粘性扩散方程eu/et-λe△u/et-div（g（｜▽Gσ＊u｜）▽u） =0的Neumann边值问题.此类方程也称为伪抛物型方程,它具有丰富的物理背景,在土壤力学、热传导及流体力学中有着广泛的应用,与图像恢复也有着密切联系.主要利用不动点方法证明其弱解的存在性,进一步证明弱解的唯一性.

英文摘要：

The Neumann problem of a class of viscous diffusion equation eu/et-λe△u/et-div（g（｜▽Gσ＊u｜）▽u） =0 is studied. Such equation is also called pseudo-parabolic equation, which has a rich physics background, and has a wide range of applications in soil mechanics, heat transfer and fluid mechanics, and also is closely related with image restoration. Using the fixed point method, the existence of weak solutions is proved, and the uniqueness of the solution is obtained.