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Consider the following initial-boundary value problem: 8²u du Pu +3 = 4- -8 Ət² Ət Əx² u(0, t) = 2, u(1, t) = 4 u(x,0)=2-1+31², (DE) (BC), (IC1), (IC2), ди Ət 0 0, t> 0, 0 < x < 1, (1,0) = 3x - 1₁ 0

Consider the following initial-boundary value problem: 8²u du Pu +3 = 4- -8 Ət² Ət Əx² u(0, t) = 2, u(1, t) = 4 u(x,0)=2-1+31², (DE) (BC), (IC1), (IC2), ди Ət 0 0, t> 0, 0 < x < 1, (1,0) = 3x - 1₁ 0

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider the following initial-boundary value problem: 8²u du +3- Ət² Ət u(0, t) = 2, u(1,0)=2-1+31², (DE) (BC), (IC1), (IC2), Ju Ət Fu -8 Əx² u(1, t) = 4 = 4- 0 << 1,t> 0, t> 0, 0 < x < 1, (1,0) = 3x - 1₁ 0<< 1. (a) Find a steady-state solution v(z); i.e., a time-independent function satisfying the differential equation and the boundary conditions. (b) Let v(z) be the steady state obtained in Part (a) and define w(z, t) = u(z,t)-(2), Write down the initial-boundary value problem satisfied by w(z,t). differential
Transcribed Image Text:Consider the following initial-boundary value problem: 8²u du +3- Ət² Ət u(0, t) = 2, u(1,0)=2-1+31², (DE) (BC), (IC1), (IC2), Ju Ət Fu -8 Əx² u(1, t) = 4 = 4- 0 << 1,t> 0, t> 0, 0 < x < 1, (1,0) = 3x - 1₁ 0<< 1. (a) Find a steady-state solution v(z); i.e., a time-independent function satisfying the differential equation and the boundary conditions. (b) Let v(z) be the steady state obtained in Part (a) and define w(z, t) = u(z,t)-(2), Write down the initial-boundary value problem satisfied by w(z,t). differential
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