### Abstract

We consider the initial value problem for a pseudodifferential equation with first order hyperbolic part, and an order $\gamma > 0$ dissipative term. Under an assumption, depending on an integer parameter $L \geq 2$ such that $2 \gamma < L$, we construct for this initial value problem a parametrix that is a Fourier integral operator of type $\rho = 1 - \gamma/L$. The assumption implies that where the principal symbol of the dissipative term is zero, the terms of order up to $L-1$ in its Taylor series also vanish.

Original language | Undefined |
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Pages (from-to) | 151-169 |

Number of pages | 19 |

Journal | Asymptotic analysis |

Volume | 43 |

Issue number | 1-2 |

Publication status | Published - 2005 |

### Keywords

- EWI-13983
- pseudodifferential initial value problem
- IR-53451
- METIS-226233
- Fourier integral operators

## Cite this

Stolk, C. C. (2005). Parametrix for a hyperbolic initial value problem with dissipation in some region.

*Asymptotic analysis*,*43*(1-2), 151-169.