非线性N-膜演化问题
The nonlinear N-membranes evolution problem
摘要：
研究了p-Laplacian方程的抛物型N-膜问题及其解的分支的全序约束，讨论了其变分解的逼近性、正则性和稳定性.我们扩展到进化的情况下的拉格朗日乘子与排序约束的重合集的特征函数的表征。我们给出了连续相关的结果，并研究了解和重合集的渐近行为，如$t \to \infty$，表明它们收敛到它们的平稳对应。
英文摘要：
The parabolic N-membranes problem for the p-Laplacian and the complete order constraint on the components of the solution is studied in what concerns the approximation, the regularity and the stability of the variational solutions. We extend to the evolutionary case the characterization of the Lagrange multipliers associated with the ordering constraint in terms of the characteristic functions of the coincidence sets. We give continuous dependence results, and study the asymptotic behavior as $t \to \infty$ of the solution and the coincidence sets, showing that they converge to their stationary counterparts.
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