### 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 |
---|---|

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 |

### Fingerprint

### Keywords

- Critical exponent
- Damped wave equation
- Diffusion phenomenon

### ASJC Scopus subject areas

- Mathematics(all)

### 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

**Critical exponent for the semilinear wave equation with time or space dependent damping.** / Nishihara, Kenji.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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

}

TY - GEN

T1 - Critical exponent for the semilinear wave equation with time or space dependent damping

AU - Nishihara, Kenji

PY - 2013

Y1 - 2013

N2 - 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.

AB - 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.

KW - Critical exponent

KW - Damped wave equation

KW - Diffusion phenomenon

UR - http://www.scopus.com/inward/record.url?scp=84883372016&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84883372016&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-00125-8_11

DO - 10.1007/978-3-319-00125-8_11

M3 - Conference contribution

SN - 9783319001241

VL - 44

SP - 239

EP - 259

BT - Springer Proceedings in Mathematics and Statistics

PB - Springer New York LLC

ER -