Use energy method to show that the following PDE p(x)un - [k(x)uz q(a)u, 0 0, u(0, x) = u(0,r) = 0, - 0≤x≤1, u(t,0)= u(t, 1) = 0, t>0 has a unique solution u = 0. Here we assume that p(a) po > 0, k(a)ko > 0, and g(x) > 0. where po and ko are constants.
Use energy method to show that the following PDE p(x)un - [k(x)uz q(a)u, 0 0, u(0, x) = u(0,r) = 0, - 0≤x≤1, u(t,0)= u(t, 1) = 0, t>0 has a unique solution u = 0. Here we assume that p(a) po > 0, k(a)ko > 0, and g(x) > 0. where po and ko are constants.
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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M3
![Use energy method to show that the following PDE
0<x<l, t>0₂
p(x)uu = [k(x)Ur]z −q(r)u,
u(0, x) = u(0,r) = 0,
&(t,0) = (t,I) = 0,
0<2<l,
t> 0
has a unique solution = 0. Here we assume that p(x) > Po > 0, k(x) > ko>0, and g(x) > 0, where po and ko are
constants.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fce32437f-acb9-4395-8261-0673e26f9c8f%2F31bab150-aeec-47f5-b801-a9f45b4345cc%2F1wke4r_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Use energy method to show that the following PDE
0<x<l, t>0₂
p(x)uu = [k(x)Ur]z −q(r)u,
u(0, x) = u(0,r) = 0,
&(t,0) = (t,I) = 0,
0<2<l,
t> 0
has a unique solution = 0. Here we assume that p(x) > Po > 0, k(x) > ko>0, and g(x) > 0, where po and ko are
constants.
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