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A note on the behavior of blowup solutions for onephase Stefan problems


It is proved that when the solution is blowup in a finite time s(uo), and u0(x) is not a constant, then the free boundary will not be blowup and the blowup set is contained in the interval [0,l0).


Moreover, when f(u,t)=u1+μ for some μ>amp;gt;0, every blowup point is isolated.


The blowup property for a system of heat equations with nonlinear boundary conditions


This paper deals with the blowup properties of solutions to the systems ut=Δu,vt=Δv in BRX(0,T) subject to nonlinear boundary conditions , in SRX(0,T).

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 A modified method bassd on the Terent'ev method of "active hydrogen" determination has been developed, by means of which both "active hydrogen" and CH3MgI addition can be determined.In this paper the procedure of the method was described in detail and a few examples of determination were given.In comparison with Kohler's method, though this method appears to be less satisfactory in accuracy, it has the advantage that the apparatus is simpler to construct and the determination easier and more rapid to be carried... A modified method bassd on the Terent'ev method of "active hydrogen" determination has been developed, by means of which both "active hydrogen" and CH3MgI addition can be determined.In this paper the procedure of the method was described in detail and a few examples of determination were given.In comparison with Kohler's method, though this method appears to be less satisfactory in accuracy, it has the advantage that the apparatus is simpler to construct and the determination easier and more rapid to be carried out.  作者根据测定活泼氢的方法,在仪器及操作程序上加以改进,使这个方法能够同时用来测定CH_3MgI试剂的加成。本文详细地描述了这一改进方法并且给出几个测定的结果。与Kohler方法相较,这个方法虽然准确度稍差一些,但所用玻璃仪器易於吹制,操作程序也比较简便。  The Austausch coefficient may be obtained by wind structure. 1902 Ekman established the wind spiral theory in the friction layer. From the observed wind spiral, we may calculate of the Austausch coefficient by this theory. 1952 considered effect of the change of pressure field with height; i. e. the thermal wind effect, and found excellent results. But, Formula holds only for the condition in the stationary current flow, or in the stationary temperature pressure field and uniform temperature pressure gradient.In... The Austausch coefficient may be obtained by wind structure. 1902 Ekman established the wind spiral theory in the friction layer. From the observed wind spiral, we may calculate of the Austausch coefficient by this theory. 1952 considered effect of the change of pressure field with height; i. e. the thermal wind effect, and found excellent results. But, Formula holds only for the condition in the stationary current flow, or in the stationary temperature pressure field and uniform temperature pressure gradient.In this paper, we consider the unstationary effect, as calculating the Austausch coefficient in the friction layer, and obtain a more general formula. Under some special constrains, it tends to be the or Ekman's formula. Then, this formula may be more accurate in calculation and more wide in application.Some calculations based on observed data by using these three different formulas are presented and compared.  摩擦层中湍流系数,利用风标的分布,可以测定之。1902年,爱克曼创立了摩擦层中风标螺线,利用风标螺线,可以测定摩擦层中的湍流系数。1953年,莱赫特曼考虑了气压场随高度的变化,即热成风的因素,获得了良好的结果。但是,莱赫特曼公式之应用,只限定于恒态吹流,或恒态均匀温压场的条件之下,方能准确使用。这样是在一般情况之下难以满足的。关于摩擦层非恒态问题,1947年赵九章、裘碧克曾经讨论过。本文仅就非恒态湍流系数测定问题予以进一步探讨。并得到了较有广泛意义之公式。而莱赫特曼公式,系属温压场恒态,温压场中温度、压力梯度在均匀情况之下,该公式之特解。爱克曼范式,系属气压场稳定,温度梯度恒态为零时,该公式之特解。这样,该公式的计算,使得湍流系数测定工作精确化和广泛化。 最后,本文作了一些实际资料的计算与分析,和讨论在自然环境中湍流系数的变化。  Bath reactions during the oxidizing period of electricfurnace steelmaking withinjection were studied. It is found that,under favourable conditions,a rate of carbon removal ofabout 0.015—0.020%C per minute(that of the normal smelting with ore beingaround 0.005% C per minute only)may be obtained;(FeO)and[O]decreasesignificantly and approach to equilibrium with[C]during the oxidizing period,andthe decrement of[O]increases proportionately with the increase of the rate ofcarbon removal.Dephosphorization during the... Bath reactions during the oxidizing period of electricfurnace steelmaking withinjection were studied. It is found that,under favourable conditions,a rate of carbon removal ofabout 0.015—0.020%C per minute(that of the normal smelting with ore beingaround 0.005% C per minute only)may be obtained;(FeO)and[O]decreasesignificantly and approach to equilibrium with[C]during the oxidizing period,andthe decrement of[O]increases proportionately with the increase of the rate ofcarbon removal.Dephosphorization during the oxidizing period is found to be rather ineffective,the average[P]removed amounts to about 0.004% only.With a supplementaryoperation of dephosphorization during the melting period,[P]can be reduced toless than 0.015% at the end of oxidizing period.However,the dephosphorizationmechanism in the case of the oxygen smelting is still not yet clear.  研究了电炉吹氧冶炼氧化期的熔池反应。观察到:在良好的操作情况下,吹氧冶炼的脱碳速度可以达到0.015—0.020%C/分钟(矿石冶炼的只有0.005%C/分钟左右);吹氧过程中,(FeO)和[O]显著降低并与[C]趋近平衡,[O]的减少量与脱碳速度间有直线关系。并注意到吹氧冶炼氧化期脱磷效果较差,平均脱磷量仅为0.004%左右;采用熔化期脱磷操作后,氧化期末[P]可以降低到小于0.015%。至于吹氧冶炼的脱磷过程,目前还不完全了解。   << 更多相关文摘 
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