Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
Number 3 please
![utt - (rux + X(a,b) Utx)x - Byt = 0, x €]0, 1[, t > 0,
Ytt (yx + X(a,b) Ytx)x+ But = 0, x €]0, 1[, t > 0,
u(0, t) = u(1, t) = y(0, t) = y(1, t) = 0, t > 0,
u(x,0) = u(x), y(x, 0) = yo(x), x €]0, 1[
u₁(x, 0) = u₁(x), yt(x, 0) = y₁(x), x €]0, 1[,
where r, 3 are positive constants and 0 < a <b<1
1. Find the energy E(t) of the system.
2. Define the appropriate Hilbert energy space H and its inner product.
(1)
3. Find the linear unbounded operator A and its domain D(A), and write the system
in the form
Ut = AU
U(0) = Uo €H](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9612a6a5-e19c-4346-ae6e-6941d4a9f0e7%2F45aff782-9af2-4d35-b8c5-e7272fedd0b9%2Fwfv9tvg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:utt - (rux + X(a,b) Utx)x - Byt = 0, x €]0, 1[, t > 0,
Ytt (yx + X(a,b) Ytx)x+ But = 0, x €]0, 1[, t > 0,
u(0, t) = u(1, t) = y(0, t) = y(1, t) = 0, t > 0,
u(x,0) = u(x), y(x, 0) = yo(x), x €]0, 1[
u₁(x, 0) = u₁(x), yt(x, 0) = y₁(x), x €]0, 1[,
where r, 3 are positive constants and 0 < a <b<1
1. Find the energy E(t) of the system.
2. Define the appropriate Hilbert energy space H and its inner product.
(1)
3. Find the linear unbounded operator A and its domain D(A), and write the system
in the form
Ut = AU
U(0) = Uo €H
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