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Consider the following initial-boundary value problem: Ju ər² (DE). (BC), (IC1), (IC2), Fu Ət² u(0, t) = 3, u(,0) = r², ди Ət = 4 - 10 (1,0) = 1, ди ər -(1,t) = 0 0 0, t> 0, 0

Consider the following initial-boundary value problem: Ju ər² (DE). (BC), (IC1), (IC2), Fu Ət² u(0, t) = 3, u(,0) = r², ди Ət = 4 - 10 (1,0) = 1, ди ər -(1,t) = 0 0 0, t> 0, 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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#3 Need A and B

Consider the following initial-boundary value problem: Pu Ju = 4 Ət² ər² u(0, t) = 3, u(t,0) = r², ди Ət (DE). (BC), (IC1), (IC2), - 10 (1,0) = 1, ди ər -(1,t) = 0 0<x< 1,t> 0, t> 0, 0<x< 1, 0 <r<1. (a) Find a steady-state solution v(r); i.e., a time-independent function satisfying the differential equation and the boundary conditions. (b) Let v(r) be the steady state obtained in Part (a) and define w(x, t) = u(z. t) - v(r). Write down the initial-boundary value problem satisfied by w(x, t). Remark: You do not need to solve w(r,t) in part (b). You only need to write the differential equation(s), boundary condition(s), and initial condition(s) for w(z,t).
Transcribed Image Text:Consider the following initial-boundary value problem: Pu Ju = 4 Ət² ər² u(0, t) = 3, u(t,0) = r², ди Ət (DE). (BC), (IC1), (IC2), - 10 (1,0) = 1, ди ər -(1,t) = 0 0<x< 1,t> 0, t> 0, 0<x< 1, 0 <r<1. (a) Find a steady-state solution v(r); i.e., a time-independent function satisfying the differential equation and the boundary conditions. (b) Let v(r) be the steady state obtained in Part (a) and define w(x, t) = u(z. t) - v(r). Write down the initial-boundary value problem satisfied by w(x, t). Remark: You do not need to solve w(r,t) in part (b). You only need to write the differential equation(s), boundary condition(s), and initial condition(s) for w(z,t).
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