非线性扩散方程Cauchy问题解的唯一性和稳定性

研究方程au/at=△A(u)+Σ^N_i=1 abⁱ(u) / ax^#em/em#+c(u)Cauchy问题解的唯一性。证明了如果u∈BV_x且A(u)严格递增,则解是唯一的。     

具强非线性源的p-Laplace方程的Cauchy问题中的1

赵俊宁  雷沛东 《数学学报》2003,46(3):529-538

The Cauchy Problem for the p-Laplacian Equation with a Nonlinear Source

In this paper we study the existence and uniqueness of positive solutions for the p-Laplaeian equation with nonlinear source eu/et=div(|Du|^p-2Du) u^-q,p＞2,0＜q＜∞ in the class of functions with some prescribed growth rate as|x|→∞. We also give a deseription of the large time behaviour and show that it is determined by thep ecompetition between the diffusion and the souree.     

Uniqueness of BV Entropy Solutions for Higher Dimensional Quasilinear Parabolic Equations with Arbitrary Degeneracy

We are concerned with the uniqueness of solutions of the Cauchy problemand a(s),b(s) are appropriately smooth.Since a(s) is allowed to have zero points, we call them points of degeneracy of (1), the equation (1) does not admit classical solutions in general. The solutions of (1) even might be discontinuous, whenever the set E = {s : a(s) = 0} includes interior points.Equations with degeneracy arise from a wide variety of diffusive processes in nature     

一类退化扩散方程组解的性质

In this paper, we prove some properties of solutions to a class of degener-ate diffusion systems which arise from modeling interacting evolution of two biological groups.