TITLE:
An Initial-Boundary Value Problem for a Modified Transitional Korteweg-de Vries Equation
AUTHORS:
Charles Bu
KEYWORDS:
Modified Transitional KdV Equation, Initial-Boundary Value Problem, Semi-Group, Local and Global Existence
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.13 No.1,
January
15,
2025
ABSTRACT: We study the following modified transitional Korteweg-de Vries equation
u
t
+f(
t
)
u
p
u
x
+
u
xxx
=0
,
(
x,t
)∈
R
+
×
R
+
, (
p≥2
is an even integer) with initial value
u(
x,0
)=g(
x
)∈
H
4
(
R
+
)
and inhomogeneous boundary value
u(
0,t
)=Q(
t
)∈
C
2
(
[
0,∞ )
)
. Under the conditions either (i)
f(
t
)≤0
,
f
′
(
t
)≥0
or (ii)
f(
t
)≤−α
where
α>0
, we prove the existence of a unique global classical solution.