基于脉冲控制的非线性抛物型方程的振动分析

Oscillation Analysis of Nonlinear Parabolic Equations Based on Impulse Control

本文研究一类带脉冲控制的非线性抛物型方程在第一类边值条件下的振动性问题,通过将多维振动问题化为一维脉冲微分不等式最终正解的存在性问题,获得该类方程一切解u(x,t)振动或者limt→+∞∫Ωu(x,t)dx=0的若干新的充分性判据.

The oscillation problems of solutions for a class of nonlinear parabolic equations with impulse control is investigated under first boundary value condition.To change the multidimensional oscillation problems into the existence problems of positive solutions of one-dimensional impulsive differential inequalities,some new sufficient criteria are obtained,which insure that any solution u（x,t）of this equation oscillates or limt→＋∞∫Ω^u（x,t）dx=0.