作者victor0410 (zero)
看板Physics
标题[问题] 四道PDE的应用题
时间Tue May 1 01:00:41 2007
恩 以下四题其实是PDE课本的习题 不过都是牵扯到物理 所以PO在这里发问
我相信对这个板的强者大大应该是轻而易举吧^^"
就麻烦板上大大指教了 谢谢 m(_ _)m
1.A flexible chain of length l is hanging from one end x=0 but oscillates
horizontally.Let the x axis point downward and the u axis point to the right.
Assume that the force of gravity at each point of the chain equals the
weight of the part of the chain below the point and is directed tangentially
along the chain.Assume the oscillations are small.Find the PDE satisfied by
the chain.
αu αu
ANS: ----=αg[(l-x)----]/αx
αt αx
2.Suppose that some particles which are suspended in a liquid medium would be
pulled down at the constant velocity V>0 by gravity in the absence of
diffusion.Taking account of the diffusion,find the equation for the
concentration of particles.Assume homogeneity in the horizontal directions x
and y.Let the z axis point upwards.
αu α^2u αu
ANS: ----=k ----- + V ----
αt αz^2 αz
3.Derive the equation of one-dimensional diffusion in a medium that is moving
along the x axis to the right at constant speed V.
αu α^2u αu
ANS: ----=k ----- - V ----
αt αx^2 αx
4.(a)Show that the temperature of a metal rod,insulated at the end x=0,
satisfies the boundary condition αu/αx = 0.
(b)Do the same for the diffusion of gas along a tube that is closed off at
the end x=0.(Use the Fick's law.)
(c)Show that the three-dimensional version of (a)(insulated solid) or (b)
(impermeable container)leads to the boundary condition αu/αn = 0.
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1F：推 Linderman:改天有空想看看写大概XD,请问您的课本是用那一本呀? 05/01 10:52
2F：→ Linderman:这些问题搞不好去问化工领域的人他们还比数学或物理的熟 05/01 10:54
3F：→ Linderman:基本上真正在搞数学PDE的人应该不是念这种方面的东西吧 05/01 10:56
4F：→ Linderman:虽然上面有非线性的PDE但是数学的人通常不管他怎麽来的 05/01 10:57
5F：→ Linderman:通常数学的都是在解您答案的问题发展非线性技巧和思想 05/01 10:59
6F：推 victor0410:Partial Differential Equations by Walter A. Strauss 05/01 15:44
7F：→ victor0410:我是数学系的 可是上面那些东西我都没学过阿 囧a 05/01 15:46
8F：推 Linderman:不会吧其实我大学也是用这本说,但是我怎麽都没印象@-@ 05/01 20:17
9F：→ Linderman:不过您放心只要是离开物理系的物理问题都是很基本的观念 05/01 20:18
10F：→ Linderman:以前我们老师通常只要这本书是跟物理有关的他全部都跳过 05/01 20:18
11F：→ Linderman:其实Strauss这本的超赞的到现在还是很受用偶而会拿来翻 05/01 20:20
12F：→ Linderman:sorry等我比较有空的时候在好好解看看吧 05/01 20:21
13F：推 victor0410:恩 感谢大大! (这是1.3 1.4的习题) 05/01 22:18
14F：推 Linderman:我不是大大@-@昨天睡前有稍微看了一下但是没有仔细去推괠 05/02 11:28
15F：→ Linderman:看了您的ip地点也许我们可以私底下讨论吧^^不过我最近忙 05/02 11:29
16F：→ Linderman:其实这地方我觉得Strauss写的太简略可以去找看工数的书 05/02 11:30