非线性退缩抛物型方程的第二边值问题产生的一个自由边值问题

A FREE BOUNDARY PROBLEM ARISED FROM NONLINEAR DEGENERATE EQUATIONS OF PARABOLIC TYPE WITH THE SECOND BOUNDARY VALUE

研究了具有阀门梯度值的非牛顿流体运动引起的非线性退缩抛物型方程的第二边值问题．由于方程的非线性和退缩性，当始值梯度为局部时，解将是局部，这就引起自由边界的产生．通过该自由边值问题的等价抛物拟变分不等式的研究，得到古典解的存在唯一性。

The authors consider a free boundary problem arised from the second boundary value problem of the flow of power law fluids with the yield stress in semiunbouned field (0,+∞), i.e. the Problem I.The authors first consider the relevant approximation free boundary problem and obtain its classical solution by means of a parabolic quasivariational inequality. Then the authors obtain the existence and uniqueness of the classical solution for the Problem I when m≥1.Finally, study the asymptotic behavior of the solution of problem I in special case.