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Arnold's Trivium
1991 Arnold's Trivium
61
61
Part of
1991 Arnold's Trivium
Problems
(1)
Problem 61
Source:
7/1/2010
What is the largest value of
t
t
t
for which the solution of the problem
∂
u
∂
t
+
u
∂
u
∂
x
=
sin
x
,
u
∣
t
=
0
=
0
\frac{\partial u}{\partial t}+u\frac{\partial u}{\partial x}=\sin x,\; u|_{t=0}=0
∂
t
∂
u
+
u
∂
x
∂
u
=
sin
x
,
u
∣
t
=
0
=
0
can be extended to the interval
[
0
,
t
)
[0,t)
[
0
,
t
)
.
trigonometry