### 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 |
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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 |

### Keywords

- Morrey spaces
- Semigroup
- Semilinear heat equations

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Yamazaki, M., & Zhou, X. (2001). Semilinear heat equations with distributions in Morrey spaces as initial data.

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