一类拟线性退化抛物方程组初边值问题正解的存在性

Existence of Positive Solutions to a Class of Quasilinear Degenerate Parabolic Systems with Initial Boundary Value Conditions

研究了带有发展型p-Laplace算子的拟线性抛物方程组在第一初边值下解的存在性.作者利用抛物正则化的方法,通过一系列的估计,证明了所得逼近解的弱收敛性,进而证明了所论问题广义解的存在性.最后作者通过构造上解,利用比较原理获得了该问题全局解存在的充分条件.

The aim of this paper is to investigate the existence of generalized solutions to coupling evolution p-Laplacian systems with the first initial boundary value conditions.The authors applied the method of parabolic regularization to prove the existence of generalized solution to the problem.By making a sequence of estimates to the solutions,the authors proved the weak convergence of the approximation solution sequence and hence testified the existence of generalized solutions.Finally,the authors found some conditions under which the solutions exists globally.