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Local Well-posedness for Semilinear Heat Equations on H type Groups
In this paper, we discuss the local existence and uniqueness for the Cauchy problem of semi heat equations with an initial data in the space Lq on H type group H p d , which has the dimension p of the center, like the argument on the Euclidean space given by F. B. Weissler. That is, the Cauchy probl...
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| Published in: | Taiwanese journal of mathematics 2018-10, Vol.22 (5), p.1091-1105 |
|---|---|
| Main Author: | |
| Format: | Article |
| Language: | English |
| Citations: | Items that this one cites Items that cite this one |
| Online Access: | Get full text |
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| Summary: | In this paper, we discuss the local existence and uniqueness for the Cauchy problem of semi heat equations with an initial data in the space Lq on H type group
H
p
d
, which has the dimension p of the center, like the argument on the Euclidean space given by F. B. Weissler. That is, the Cauchy problem
{
(
∂
t
−
Δ
H
p
d
)
u
(
g
,
t
)
=
|
u
|
r
−
1
u
,
g
∈
H
p
d
,
t
>
0
,
u
(
g
,
0
)
=
u
0
(
g
)
∈
L
q
(
H
p
d
)
has a unique solution if q > N(r − 1)/2 (q = N (r − 1)/2) and q ≥ r (q > r), where r > 1 and N = 2d + 2p is the homogeneous dimension of
H
p
d
. |
|---|---|
| ISSN: | 1027-5487 2224-6851 |
| DOI: | 10.11650/tjm/180301 |