Abstract
AbstractWe show that the Hunter–Saxton equation $$u_t+uu_x=\frac{1}{4}\big (\int _{-\infty }^x \hbox {d}\mu (t,z)- \int ^{\infty }_x \hbox {d}\mu (t,z)\big )$$
u
t
+
u
u
x
=
1
4
(
∫
-
∞
x
d
μ
(
t
,
z
)
-
∫
x
∞
d
μ
(
t
,
z
)
)
and $$\mu _t+(u\mu )_x=0$$
μ
t
+
(
u
μ
)
x
=
0
has a unique, global, weak, and conservative solution $$(u,\mu )$$
(
u
,
μ
)
of the Cauchy problem on the line.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computational Mathematics,Mathematics (miscellaneous),Theoretical Computer Science
Cited by
4 articles.
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