一类非散度型退化抛物方程广义解的存在性

讨论一类非散度型退化抛物方程的初边值问题. 利用抛物正则化方法, 证明了该问题广义解的存在性. 对初边值和方程做了两重正则化, 并分别进行了一系列的估计. 利用分析方法, 证明了所得逼近解序列的弱收敛性, 进而证明了其弱解的存在性.

Existence of Solutions to a Class of Degenerate Parabolic Equations in Non-divergence Form

The present paper discusses the existence of weak solutions to the initial and boundary value problem of a class of degenerate parabolic equations in non-divergence form. The authors applied the method of parabolic regularization to prove the existence of weak solutions to the problem. By carefully analyzing the approximate solutions to the problem, the authors made a sequence of estimates to the solutions and proved the weak convergence of the approximation solution sequence and hence testified the existence of weak solutions.