### 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 |

### Fingerprint

### Keywords

- Morrey spaces
- Semigroup
- Semilinear heat equations

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Hokkaido Mathematical Journal*,

*30*(3), 537-571. https://doi.org/10.14492/hokmj/1350912790

**Semilinear heat equations with distributions in Morrey spaces as initial data.** / Yamazaki, Masao; Zhou, Xiaofang.

Research output: Contribution to journal › Article

*Hokkaido Mathematical Journal*, vol. 30, no. 3, pp. 537-571. https://doi.org/10.14492/hokmj/1350912790

}

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 -