PS2soln - f LocT/wm g —————__l._._ MATH 412:...

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Unformatted text preview: f LocT/wm g —————__l._._ MATH 412: Problem Set 2 due Thursday, February 7, 2008 1. Strauss 2.2 #2 - energy and momentum for wave equation 2. Strauss 2.2 #5 — damped wave equation 3. Consider the following transport-decay equation for Mrs, t): at + can: 2 —,\u Where A > D is a constant. By making an appropriate change of variables similar to What we discussed in class, convert this to an ordinary differential equation (ODE). Then solve that equation, remembering that any constants could be functions of the other variable. From this obtain a solution ii(rr:, t). Show also that this equation can be solved by making the following change of dependent variable (the function itself): w(m,t) = n(a‘,t)e)‘t How do you interpret this? 4. Strauss 2.3 #6 - comparison principle for heat equation HINT: define w(mj t) : nix, t) — ii(:r, t), and use the Maximum Principle for the heat equation (p.42) 5. Strauss 2.3 #8 - radiative boundary condition 6. Strauss 2.4 #1 - difinsion equation 7. Strauss 2.4 #11 - even and odd initial conditions Version 1.1 P” :‘g‘Q/fifkwyg wfi’wak) I @252; Z Dawé/ML SLMHH‘F 4Myflx$$®r€~ Q? (53/494 L457 3 _ LHXM¥+IL 6 y}: / . 2 ‘ M 2/6 Die/M 4%”? '1 Mafi 4545444“ ‘ E I E V 4'" er/ 1:: M3“? flak;— OCR—k2»!— "‘_Z_. LCJMJG Mfg“ :M-x—X’ Mkkkiflfiék:éé% W ’2’ gwlvw's; $55? Whgfixxl”fU/P F>© (a’dfi‘rzbu'rx BONE GAO/>7 (/fl/fi’ HC§M+MKX3 w‘o/Q Mk ‘AUC 9/ {>3 6 gag—(EMPKgO/K : _ )2 )2 34; J, E z édv‘ 904$“ "CflMWC/X "I" fiacf/ J7, PL )3 Lflm 3L _,L a ' dé Wit/K “5 Vflxfifl/y/A/ " '— flébg/ ’7 >0 32 27/ Q 0 L43L;9[ i "2 E étd‘eueg Am 33-72556 $692 w‘ 9 We 5% Wamuw $ 141ka 74,. +9“) 7521; M/A7+\ 4 vkfl (#742 EC; MflZ—A f. K/flg‘?) ym'r“U'-€ ...
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This note was uploaded on 07/23/2008 for the course MATH 412 taught by Professor Belmonte during the Spring '08 term at Pennsylvania State University, University Park.

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PS2soln - f LocT/wm g —————__l._._ MATH 412:...

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