2. Compare the solution with the general solution of the wave equation on [0, a] × [0, b], with same boundary conditions and same v: what is a key difference that you notice?
2. Compare the solution with the general solution of the wave equation on [0, a] × [0, b], with same boundary conditions and same v: what is a key difference that you notice?
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ONLY QUESTION 2 NEEDs TO BE SOLVED
![Question 5. Use the method of separation of variables to derive the
general solution (show all the details, explain!) of the diffusion equation
(propagation of heat) on the rectangle [0, a] × [0, b]:
Uų = v²Au,
with zero boundary conditions. Then, answer the following questions.
1. What happens as the time t →? What does it mean physically?
2. Compare the solution with the general solution of the wave equation
on [0, a] × [0, b], with same boundary conditions and same v: what is a
key difference that you notice?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F74ca7159-d1ce-4abe-9c24-5b17bb77ce00%2F49d9a06b-9e34-40fa-a96a-f84c9c0c6acc%2Fsol3see_processed.png&w=3840&q=75)
Transcribed Image Text:Question 5. Use the method of separation of variables to derive the
general solution (show all the details, explain!) of the diffusion equation
(propagation of heat) on the rectangle [0, a] × [0, b]:
Uų = v²Au,
with zero boundary conditions. Then, answer the following questions.
1. What happens as the time t →? What does it mean physically?
2. Compare the solution with the general solution of the wave equation
on [0, a] × [0, b], with same boundary conditions and same v: what is a
key difference that you notice?
Expert Solution
Step 1
(2)
Given:
The coordinates of the rectangle are .
The diffusion equation is .
Introduction:
The diffusion equation is a parabolic partial differential equation. It describes the macroscopic behavior of many micro-particles in Brownian motion, resulting from the random movements and collisions of the particles
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