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

2003/12/05 by Christiaan C. Stolk, Stolk, Christiaan C.
Mathematics · #35S10 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #advanced mathematical theories #math.AP #msc:35S10

paper · pdf · doi:10.48550/arxiv.math/0312119

19 pages

arxiv created 2003/12/05 · openalex publication_date 2003/12/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 ≥ 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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