# Parametrix for a hyperbolic initial value problem with dissipation in some region

C.C. Stolk

7 Citations (Scopus)

## 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 151-169 19 Asymptotic analysis 43 1-2 Published - 2005

## Keywords

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