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

Christiaan C. Stolk
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Abstract

We consider the initial value problem for a pseudodifferential equation with first order hyperbolic part, and an order $γ> 0$ dissipative term. Under an assumption, depending on an integer parameter $L \geq 2$ such that $2 γ< L$, we construct for this initial value problem a parametrix that is a Fourier integral operator of type $ρ= 1 - γ/L$. 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.

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Christiaan C. Stolk. 2003-12-05. Parametrix for a hyperbolic initial value problem with dissipation in some region. https://arxiv.org/abs/math/0312119

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