一般的一维滤流方程的第三边值问题(英文)

The Third Boundary Value Problem for General One-Dimensional Filtration Equation

本文在半空间中研究一般的一维滤流方程的第三边值问题.这个问题描述了土壤中有非线性扩散、对流(蒸发)和吸收相互作用而且地表有供水或抽水时地下水的运动.我们证明了唯一弱解的存在性,这个弱解可以用单调不增的正解序列来逼近,在初值有正下界的情况下,我们证明了古典解局部存在性.

This paper deals with the third boundary value problem for general one-dimensional filtration equation in half-space. It describes the interaction of nonlinear diffusion, convection (evaporation), and absorption of soil with water supply or deprivation on ground surface. It is proved that there exists an unique weak solution and it can be approximated by a monotonically nonincreasing positive solution sequence. In the case that initial data has positive infimum, the classical slution exists locally.