TITLE:
A Modified Transitional Korteweg-De Vries Equation: Posed in the Quarter Plane
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.12 No.7,
July
31,
2024
ABSTRACT: This paper is concerned with a modified transitional Korteweg-de Vries equation
u
t
+f(
t
)
u
2
u
x
+
u
xxx
=0
,
(
x,t
)∈
R
+
×
R
+
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 1)
f(
t
)≤0
,
f
′
(
t
)≥0
or 2)
f(
t
)≤−α
where
α>0
, we prove the existence of a unique global classical solution.