一类非散度抛物型方程混合问题解趋于零的充分必要条件

Q2 Mathematics

Transactions of the Moscow Mathematical Society Pub Date : 2014-11-05 DOI:10.1090/S0077-1554-2014-00233-8

Yu. A. Alkhutov, V. N. Denisov

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引用次数: 6

摘要

考虑一类非散度形式的均匀抛物型二阶方程在圆柱域上的第一边值问题。解在柱面上满足齐次狄利克雷条件，且初始函数有界。我们证明了如果方程的系数满足局部和全局Dini条件，那么解稳定于零的充分必要条件与热方程的类似条件是一致的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Necessary and sufficient condition for the stabilization of the solution of a mixed problem for nondivergence parabolic equations to zero

We consider the first boundary value problem in a cylindrical domain for a uniformly parabolic second-order equation in nondivergence form. The solution satisfies the homogeneous Dirichlet condition on the lateral surface of the cylinder, and the initial function is bounded. We show that if the coefficients of the equation satisfy the local and global Dini conditions, then a necessary and sufficient condition for the stabilization of the solution to zero coincides with a similar condition for the heat equation.

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Transactions of the Moscow Mathematical Society Mathematics-Mathematics (miscellaneous)

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期刊介绍： This journal, a translation of Trudy Moskovskogo Matematicheskogo Obshchestva, contains the results of original research in pure mathematics.