Abstract
This paper is a continuous study to the paper [27]. Here we consider in Morrey spaces the Cauchy problem of the general semilinear heat equation with an external force. Both the external force and initial data belong to suitable Morrey spaces. When the norm of the external force is small, we proved the unique existence of small solution to the corresponding stationary problem. Moreover, if the initial data is close enough to the stationary solution, we verified the time-global solvability of the Cauchy problem, which leads to the stability of the small stationary solution.
| Original language | English |
|---|---|
| Pages (from-to) | 537-571 |
| Number of pages | 35 |
| Journal | Hokkaido Mathematical Journal |
| Volume | 30 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 2001 Jan 1 |
| Externally published | Yes |
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Keywords
- Morrey spaces
- Semigroup
- Semilinear heat equations
ASJC Scopus subject areas
- Mathematics(all)
Cite this
Semilinear heat equations with distributions in Morrey spaces as initial data. / Yamazaki, Masao; Zhou, Xiaofang.
In: Hokkaido Mathematical Journal, Vol. 30, No. 3, 01.01.2001, p. 537-571.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Semilinear heat equations with distributions in Morrey spaces as initial data
AU - Yamazaki, Masao
AU - Zhou, Xiaofang
PY - 2001/1/1
Y1 - 2001/1/1
N2 - This paper is a continuous study to the paper [27]. Here we consider in Morrey spaces the Cauchy problem of the general semilinear heat equation with an external force. Both the external force and initial data belong to suitable Morrey spaces. When the norm of the external force is small, we proved the unique existence of small solution to the corresponding stationary problem. Moreover, if the initial data is close enough to the stationary solution, we verified the time-global solvability of the Cauchy problem, which leads to the stability of the small stationary solution.
AB - This paper is a continuous study to the paper [27]. Here we consider in Morrey spaces the Cauchy problem of the general semilinear heat equation with an external force. Both the external force and initial data belong to suitable Morrey spaces. When the norm of the external force is small, we proved the unique existence of small solution to the corresponding stationary problem. Moreover, if the initial data is close enough to the stationary solution, we verified the time-global solvability of the Cauchy problem, which leads to the stability of the small stationary solution.
KW - Morrey spaces
KW - Semigroup
KW - Semilinear heat equations
UR - http://www.scopus.com/inward/record.url?scp=85010035135&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85010035135&partnerID=8YFLogxK
U2 - 10.14492/hokmj/1350912790
DO - 10.14492/hokmj/1350912790
M3 - Article
AN - SCOPUS:85010035135
VL - 30
SP - 537
EP - 571
JO - Hokkaido Mathematical Journal
JF - Hokkaido Mathematical Journal
SN - 0385-4035
IS - 3
ER -