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Energy dissipation identity for a linearly damped string
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)
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Area of mathematics
Analysis
Partial differential equation
Wave equation
Wave equation on a string
Linearly damped string
Created
2026-09-24
Updated
2026-09-24
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For fixed endpoints and
E
(
t
)
=
2
1
∫
0
1
(
y
t
2
+
y
x
2
)
d
x
,
(1)
integration by parts
and the
damped wave equation
give
E
′
(
t
)
=
−
∫
0
1
y
t
2
d
x
≤
0.
(2)
Ancestors
(8)
Linearly damped string
Wave equation on a string
Wave equation
Partial differential equation
Analysis
Area of mathematics
Mathematics
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(1)
Past exam of the mathematics course of the University of Cambridge
/
2024
/
ib
/
Paper 3
/
14B
/
Solution
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