抛物型时滞偏微分方程解振动的充要条件

讨论了一类多滞量延迟时滞抛物型偏微分方程解的振动性质 ,利用平均值方法将所讨论的偏微分方程转化为时滞微分方程的问题 ,获得了其一切解振动的充要条件 ;所得的条件将时滞偏微分方程解的振动判别问题转化为时滞微分方程解的振动判别问题 ;结果充分显示了解的振动是由时滞量引起的 ,指出了其与普通抛物型偏微分方程解的质的差异 ;同时也指出了时滞在振动中的影响作用以及时滞偏微分方程解的振动性质在生物学、医学、工程学、化学、物理学等学科中的广泛应用

Necessary and Sufficient Condition for Oscillations of Parabolic Equations

Oscillatory properties of solutions of certain delayed parabolic partial differential equations are investigated. It inverted the discussed delayed partial differential equations into delayed ordinary differential equations by the method of the mean, a series of necessary and sufficient conditions for oscillations of the equations are established. The results fully indicated that the oscillations are caused by the delay. This is one important conclusion and hence it revealed the decisive influence in the oscillations of the solution to the delayed parabolic differential equations and also pointed out the essential differences between the equations and those equations without delay.The results also revealed the relation between these equations and ordinary differential equations with delay. The paper also showed that the oscillations of the solutions to the delayed partial differential equations have wide applications in such subjects as biology, medicine, engineering, chemistry and physics.