论文标题
对重型函数驱动退化扩散方程的数值研究
A numerical study of an Heaviside function driven degenerate diffusion equation
论文作者
论文摘要
我们分析了一个非线性退化抛物线问题，该问题的扩散系数是溶液本身与给定目标函数的距离的重物函数。我们表明，该模型的行为是一种进化的变异不平等，目标是障碍物：在适当的假设下，从目标上方的初始状态开始，解决方案及时向渐近解决方案演变，最终与目标本身的一部分接触。我们还使用精确的重质函数或定期近似值研究了解决该问题的有限差异方法，显示了一些数值测试的结果。
We analyze a nonlinear degenerate parabolic problem whose diffusion coefficient is the Heaviside function of the distance of the solution itself from a given target function. We show that this model behaves as an evolutive variational inequality having the target as an obstacle: under suitable hypotheses, starting from an initial state above the target the solution evolves in time towards an asymptotic solution, eventually getting in contact with part of the target itself. We also study a finite difference approach to the solution of this problem, using the exact Heaviside function or a regular approximation of it, showing the results of some numerical tests.
