### Abstract

Since the damped wave equation has the diffusion phenomenon, the critical exponent is expected to be the same as that for the corresponding diffusive equation with semilinear term. Therefore, we first remember the basic facts on the diffusion phenomenon. Then, from this point of view, we can conjecture the critical exponent for the damped wave equation and state several results. Finally, the small data global existence of solutions is shown in the supercritical exponent, while no global existence for some data is done in the critical and subcritical exponents. The latter part will be applied to the semilinear damped wave equation with quadratically decaying potential.

Original language | English |
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Title of host publication | Springer Proceedings in Mathematics and Statistics |

Publisher | Springer New York LLC |

Pages | 239-259 |

Number of pages | 21 |

Volume | 44 |

ISBN (Print) | 9783319001241 |

DOIs | |

Publication status | Published - 2013 |

### Keywords

- Critical exponent
- Damped wave equation
- Diffusion phenomenon

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

*Springer Proceedings in Mathematics and Statistics*(Vol. 44, pp. 239-259). Springer New York LLC. https://doi.org/10.1007/978-3-319-00125-8_11