陈祖墀偏微分方程第4版习题3参考解答

[pde]陈祖墀偏微分方程第4版习题3-01 特征线法求波动方程       https://mp.weixin.qq.com/s?__biz=MzU1OTQxNTUwNg==&mid=2247508809&idx=7&sn=36e55bd99facd3ad5dbb6e71032ee1d1&chksm=fc154af4cb62c3e2a5a5b07b2acaad1c83872e74b68d2e3ab6ab17be371bc3ff45c26bed577c

[pde]陈祖墀偏微分方程第4版习题3-02 波动方程的能量守恒与能量均分定理       https://mp.weixin.qq.com/s?__biz=MzU1OTQxNTUwNg==&mid=2247508809&idx=6&sn=155a64df03354b04973435108074d4d3&chksm=fc154af4cb62c3e29957b8a957d288fb454396251eb25b2eb5389efe104f76c052493745cf4d

[pde]陈祖墀偏微分方程第4版习题3-03 Goursat 问题的求解公式       https://mp.weixin.qq.com/s?__biz=MzU1OTQxNTUwNg==&mid=2247508809&idx=5&sn=650a220a68919fcc52cff944e5f5737b&chksm=fc154af4cb62c3e2c87293e6bdf2def5b1e03a71a81ee2fece84f63a3edc43a45efdebb613fe

[pde]陈祖墀偏微分方程第4版习题3-04 非齐次 Goursat 问题有解的充分必要条件       https://mp.weixin.qq.com/s?__biz=MzU1OTQxNTUwNg==&mid=2247508809&idx=4&sn=2d2d9ba8f328de8cc908b5be810f02a1&chksm=fc154af4cb62c3e2944ae6f5b71497e029dfc0bf5d7dcb397ceb544d918b45a639fb0642b041

[pde]陈祖墀偏微分方程第4版习题3-05 变系数双曲方程的求解       https://mp.weixin.qq.com/s?__biz=MzU1OTQxNTUwNg==&mid=2247508809&idx=3&sn=08ee66cd04823b8009f0b3d2cf31e2a4&chksm=fc154af4cb62c3e2c0c9e061985cee21ab32373f9e9643850590bb0a60e4ae19cfa3d8189f4c

[pde]陈祖墀偏微分方程第4版习题3-06 圆锥形枢轴的纵振动       https://mp.weixin.qq.com/s?__biz=MzU1OTQxNTUwNg==&mid=2247508809&idx=2&sn=c2412e8358c6385e58a0f2dc5bd99a4e&chksm=fc154af4cb62c3e242146473a227ac3b6c913e3d4484c2e6fcebc1b1d4ed107a4b9c329f86ac

[pde]陈祖墀偏微分方程第4版习题3-07 三维波动方程的球对称解       https://mp.weixin.qq.com/s?__biz=MzU1OTQxNTUwNg==&mid=2247508809&idx=1&sn=47fe8750f3d21d0d29c9590b0e998421&chksm=fc154af4cb62c3e2cfd238357251287f9d3c755171a2aa39b369e15a82d2ae29df2987411d28

[pde]陈祖墀偏微分方程第4版习题3-08 半直线上波动方程的混合问题的相容性条件    https://mp.weixin.qq.com/s?__biz=MzU1OTQxNTUwNg==&mid=2247508811&idx=8&sn=11f258a1173912798a11fedb601d5284&chksm=fc154af6cb62c3e0a2fa20ee24063d446bda2ab41d0ecc6b4e67b00ba367d100b0e64bc4e4ce

[pde]陈祖墀偏微分方程第4版习题3-09 波动方程初值问题的 Duhamel 原理 (齐次化原理)    https://mp.weixin.qq.com/s?__biz=MzU1OTQxNTUwNg==&mid=2247508811&idx=7&sn=2d1b3fdc1db08ce1b460f926dfb10fe2&chksm=fc154af6cb62c3e06fd175b30a3f7b1e1d67716ac0f588916fa15cfcbbb417ba8d2fcc0e512b

[pde]陈祖墀偏微分方程第4版习题3-10 非齐次波动方程初值问题的求解公式       https://mp.weixin.qq.com/s?__biz=MzU1OTQxNTUwNg==&mid=2247508811&idx=6&sn=989a4f6e6a4710ec2caa01ff67421312&chksm=fc154af6cb62c3e05bac9afd6c26b20194b5fc92d6c3a24beefc040975eb14770fe31631e14a

[pde]陈祖墀偏微分方程第4版习题3-11 非齐次波动方程非齐次初值的 Cauchy 问题的求解公式 https://mp.weixin.qq.com/s?__biz=MzU1OTQxNTUwNg==&mid=2247508811&idx=5&sn=74f894ac3f63523238fb2b288ce48cde&chksm=fc154af6cb62c3e0d71446f8f4d38d0327d4e0af81bf7ee27e45a7cc62bf1b03a01d9b4d7f5a

[pde]陈祖墀偏微分方程第4版习题3-12 用分离变量法求解波动方程的初边值问题       https://mp.weixin.qq.com/s?__biz=MzU1OTQxNTUwNg==&mid=2247508811&idx=4&sn=bf8ce8521368b9f9c4625d86f9c7d8af&chksm=fc154af6cb62c3e0e062f370631432d354e4b68c498538bdfdb8b61e806b7083eb2f2213b671

[pde]陈祖墀偏微分方程第4版习题3-13 用分离变量法和特征函数展开法求解波动方程的初边值问题       https://mp.weixin.qq.com/s?__biz=MzU1OTQxNTUwNg==&mid=2247508811&idx=3&sn=37102a7a397ce99bf555e6c6be29687b&chksm=fc154af6cb62c3e079033900ccc2a1d0f95dd0d339de929790b7dc4b22bbd3fd204865b4afed

[pde]陈祖墀偏微分方程第4版习题3-15 用分离变量法求解一个四阶偏微分方程    https://mp.weixin.qq.com/s?__biz=MzU1OTQxNTUwNg==&mid=2247508811&idx=2&sn=93bc96c255808bb7fca5e09d7b883f27&chksm=fc154af6cb62c3e008802654208e3c710348cd8d23088f5ec1ac98ada313fdffe9c6ceb6be38

[pde]陈祖墀偏微分方程第4版习题3-16 用分离变量法求解双曲方程的混合问题    https://mp.weixin.qq.com/s?__biz=MzU1OTQxNTUwNg==&mid=2247508811&idx=1&sn=e86cd90df0a2f6245150c8476bf735c8&chksm=fc154af6cb62c3e0673095cb60be0a426c1b03f75b032866e5da522af543d2b47425b4e4af1f

[pde]陈祖墀偏微分方程第4版习题3-17 用分离变量法求解热方程的混合问题       https://mp.weixin.qq.com/s?__biz=MzU1OTQxNTUwNg==&mid=2247508814&idx=8&sn=1fa963e6e68019e85512bfc7d9c6b85d&chksm=fc154af3cb62c3e5284cc477b9d058444c92e3c98f950a5951e42996ea36be557c2a832253a6

[pde]陈祖墀偏微分方程第4版习题3-18 用分离变量法求解二维波动方程在矩形区域中的混合问题    https://mp.weixin.qq.com/s?__biz=MzU1OTQxNTUwNg==&mid=2247508814&idx=7&sn=003b52cdc886e44d7d7e33a1ae5753fb&chksm=fc154af3cb62c3e5406e07439fbe57f19dfbc6d490c705d20b1cc8e9aab69f3bc9bea6c0e91e

[pde]陈祖墀偏微分方程第4版习题3-19 Sturm-Liouville 特征值问题的特征函数的加权正交性    https://mp.weixin.qq.com/s?__biz=MzU1OTQxNTUwNg==&mid=2247508814&idx=6&sn=f18fcefc4130886a2e5706cfbc1488b3&chksm=fc154af3cb62c3e5591b0e81e5c979311d4a9644bdef40ea786ad5666cdfc05ab0849cb72456

[pde]陈祖墀偏微分方程第4版习题3-20 特征函数系的完备性       https://mp.weixin.qq.com/s?__biz=MzU1OTQxNTUwNg==&mid=2247508814&idx=5&sn=45e6a8216536db23842b75bd481e49e7&chksm=fc154af3cb62c3e5e6a7224da00f7d5ac05ce5219c7e1ce891120d7aeee6d881adb924d2c53d

[pde]陈祖墀偏微分方程第4版习题3-21 双曲方程的能量积分函数及解的唯一性    https://mp.weixin.qq.com/s?__biz=MzU1OTQxNTUwNg==&mid=2247508814&idx=4&sn=789c5807d6091d8ef2cb5a93567ed157&chksm=fc154af3cb62c3e58c041f5693b8f0d15f3bd6e84c94f34c3481ac783ea1f38be87841177bee

[pde]陈祖墀偏微分方程第4版习题3-22 非齐次波动方程的混合问题的 Duhamel 原理 (齐次化原理)   https://mp.weixin.qq.com/s?__biz=MzU1OTQxNTUwNg==&mid=2247508814&idx=3&sn=71ae3047f7161947d337606f252eb9b5&chksm=fc154af3cb62c3e5b8d99888312a46c4efcd4d1cc4e15c668547c8cf5ebac4ac55666e7c75d6

[pde]陈祖墀偏微分方程第4版习题3-23 单位圆上的 Dirichlet 问题的经典解    https://mp.weixin.qq.com/s?__biz=MzU1OTQxNTUwNg==&mid=2247508814&idx=2&sn=e16d1eaead24fbc16dbaeac607ee682f&chksm=fc154af3cb62c3e54d26916ed5cfc44f0609ac63ab416af5e0ba7343aaf5e851ff6c538d4360

[pde]陈祖墀偏微分方程第4版习题3-24 麦克斯韦方程组中电场和磁场都满足波动方程       https://mp.weixin.qq.com/s?__biz=MzU1OTQxNTUwNg==&mid=2247508814&idx=1&sn=d4c6da4f2df95363d420dda1f8ab37bc&chksm=fc154af3cb62c3e5c8961e3b6bba313617291901f47ffc5c36213ca09e1b23ec348f6622238a

[pde]陈祖墀偏微分方程第4版习题3-25 Kirchhoff 公式求解三维波动方程的初值问题    https://mp.weixin.qq.com/s?__biz=MzU1OTQxNTUwNg==&mid=2247508816&idx=8&sn=936e812f86c823daaa9f75532f7088f6&chksm=fc154aedcb62c3fb52627d18177df89bfd6c8d2f62090e5518a35905f251275f5b727ef78f97

[pde]陈祖墀偏微分方程第4版习题3-26 n 维波动方程的解的球面平均函数满足欧拉-泊松-达布方程       https://mp.weixin.qq.com/s?__biz=MzU1OTQxNTUwNg==&mid=2247508816&idx=7&sn=3c099d28180ad4ed13a3d3c9f80cf377&chksm=fc154aedcb62c3fb57dcc9eaa1e1ccf060d3497fdf9cd8d1bad1aba04efb61c343aed928fcec

[pde]陈祖墀偏微分方程第4版习题3-27 三维波动方程初值问题解的衰减估计       https://mp.weixin.qq.com/s?__biz=MzU1OTQxNTUwNg==&mid=2247508816&idx=6&sn=1c7312908ff6a9027c129f0e518fadae&chksm=fc154aedcb62c3fb4aa8d290de1476c8ec91b8f67366401747ef17301ed28a00bb45f314d866

[pde]陈祖墀偏微分方程第4版习题3-28 降维法求一维波动方程的解       https://mp.weixin.qq.com/s?__biz=MzU1OTQxNTUwNg==&mid=2247508816&idx=5&sn=e2ab1147cc4133ba61b05c509637d82c&chksm=fc154aedcb62c3fbd0b10c20e40b4b2c3436f1aa67abb6bfa7513cef75991d1c0915d6981626

[pde]陈祖墀偏微分方程第4版习题3-29 三维波动方程经典解的存在性       https://mp.weixin.qq.com/s?__biz=MzU1OTQxNTUwNg==&mid=2247508816&idx=4&sn=5ff92cc822cb6ad170d140fa527b68bc&chksm=fc154aedcb62c3fb463e6fe431822551b11176855cabea9dd9fd5a70b62cd6b619cdae0016b9

[pde]陈祖墀偏微分方程第4版习题3-30 二维波动方程初值问题的求解       https://mp.weixin.qq.com/s?__biz=MzU1OTQxNTUwNg==&mid=2247508816&idx=3&sn=fe2d5252c3751ff1ff3bec2b38494fe4&chksm=fc154aedcb62c3fbdc666190feead0c4f4b78b2f792eca841a83fc9de2417823027094e10364

[pde]陈祖墀偏微分方程第4版习题3-31 二维波动方程的球对称解       https://mp.weixin.qq.com/s?__biz=MzU1OTQxNTUwNg==&mid=2247508816&idx=2&sn=4aa6acbe9700e5adcdad05ffee17deb9&chksm=fc154aedcb62c3fbe382a3ba899508cf40149659ae4f00a1dbebc171df0d47df25e52c99f549

[pde]陈祖墀偏微分方程第4版习题3-32 带零阶项的二维波动方程的求解       https://mp.weixin.qq.com/s?__biz=MzU1OTQxNTUwNg==&mid=2247508816&idx=1&sn=03352ba29e5898c26ace55a5147681d2&chksm=fc154aedcb62c3fb883903062850c8a02c5a95555fe7c70d68788c9429abea45d08e225bf633

[pde]陈祖墀偏微分方程第4版习题3-33 二维波动方程关于矩形区域的决定区域    https://mp.weixin.qq.com/s?__biz=MzU1OTQxNTUwNg==&mid=2247508818&idx=8&sn=0d3ecc130dcba373fe102bb5d593055d&chksm=fc154aefcb62c3f9c9db4dda8bd7604e9194af0f955ba524a3eddb27b1ddc05318996af79634

[pde]陈祖墀偏微分方程第4版习题3-34 二维非齐次波动方程初值问题的求解公式       https://mp.weixin.qq.com/s?__biz=MzU1OTQxNTUwNg==&mid=2247508818&idx=7&sn=156ef0207b25674581ddad69b96f32ce&chksm=fc154aefcb62c3f9ea3c63a5b842b23c5be710d174949fd3eb7bd688ccb6f415cc571e8b57fb

[pde]陈祖墀偏微分方程第4版习题3-35 用降维法求解二维非齐次波动方程的初值问题       https://mp.weixin.qq.com/s?__biz=MzU1OTQxNTUwNg==&mid=2247508818&idx=6&sn=3d6c9f446da2249e21bb00fabeaf8c0e&chksm=fc154aefcb62c3f95ad4b6e39968bd37c4a4b0152b6e91b7c57be2952ef4fb853fc0fc21ce61

[pde]陈祖墀偏微分方程第4版习题3-36 三维非齐次波动方程初值问题的求解       https://mp.weixin.qq.com/s?__biz=MzU1OTQxNTUwNg==&mid=2247508818&idx=5&sn=0ad45ef8c14ef30ecde9464760478104&chksm=fc154aefcb62c3f9d2ee83cb6cf0eed8d2060af35796de72725ae734cf326a402a433e1b34c9

[pde]陈祖墀偏微分方程第4版习题3-37 二维非齐次波动方程的初边值问题关于外力的稳定性    https://mp.weixin.qq.com/s?__biz=MzU1OTQxNTUwNg==&mid=2247508818&idx=4&sn=277a0ff3233661a8e87e6ac07a9d3c03&chksm=fc154aefcb62c3f9419e95e4519e887f42272e5f7b11bdb06a677a0267758d273ec4a0b41d9b

[pde]陈祖墀偏微分方程第4版习题3-38 受摩擦力作用的端点固定的有界弦的强迫振动, 其能量是减少的  https://mp.weixin.qq.com/s?__biz=MzU1OTQxNTUwNg==&mid=2247508818&idx=3&sn=1cdb00da2b768e7786595c762564b60c&chksm=fc154aefcb62c3f9c0a0ad590a3462e8498492fca2f32fe48ba7cb52c6fd63ecf5f40b3cf4f8

[pde]陈祖墀偏微分方程第4版习题3-39 一个双曲方程关于外力的稳定性       https://mp.weixin.qq.com/s?__biz=MzU1OTQxNTUwNg==&mid=2247508818&idx=2&sn=3a4f2bda927dd9a101926cf5ecc58c01&chksm=fc154aefcb62c3f9a0773bae7ab67f1885cea792518e37f9cb9f46fba4247bcee771904605fc

[pde]陈祖墀偏微分方程第4版习题3-40 无外力的薄膜的微小振动, 其能量的估计    https://mp.weixin.qq.com/s?__biz=MzU1OTQxNTUwNg==&mid=2247508818&idx=1&sn=eabf98687fff4075486e5a39d62e5aa4&chksm=fc154aefcb62c3f92d3a646cd364b744ac7828248545d1c02939ccf092112ebbf6b4b525cb3e

[pde]陈祖墀偏微分方程第4版习题3-41 二维齐次波动方程在特征锥上的能量估计       https://mp.weixin.qq.com/s?__biz=MzU1OTQxNTUwNg==&mid=2247508820&idx=8&sn=05fff1b1318c1bb5de58dfc2fe1b1f97&chksm=fc154ae9cb62c3ff1949298d6782d058e273cb14548b4fda00b4945bc1e006c522d7b9a4de89

[pde]陈祖墀偏微分方程第4版习题3-42 二维波动方程的初值问题关于初值的稳定性    https://mp.weixin.qq.com/s?__biz=MzU1OTQxNTUwNg==&mid=2247508820&idx=7&sn=2f5bdaa99e2c8cd7346fd936e4446e83&chksm=fc154ae9cb62c3ff73bff31e9bc1448a03d79129dd7b7efb68ca480408342ecfd2221e602ee2