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SIGMA, 2020, Volume 16, 009, 21 pp. (Mi sigma1546)  

New Examples of Irreducible Local Diffusion of Hyperbolic PDE's

Victor A. Vassilievab

a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
b National Research University Higher School of Economics, Moscow, Russia

Abstract: Local diffusion of strictly hyperbolic higher-order PDE's with constant coefficients at all simple singularities of corresponding wavefronts can be explained and recognized by only two local geometrical features of these wavefronts. We radically disprove the obvious conjecture extending this fact to arbitrary singularities: namely, we present examples of diffusion at all non-simple singularity classes of generic wavefronts in odd-dimensional spaces, which are not reducible to diffusion at simple singular points.

Keywords: wavefront, discriminant, critical point, morsification, vanishing cycle, hyperbolic PDE, fundamental solution, lacuna, sharp front, diffusion, Petrovskii condition.

Funding Agency Grant Number
Russian Science Foundation 16-11-10316
This work was supported by Russian Science Foundation grant 16-11-10316.


DOI: https://doi.org/10.3842/SIGMA.2020.009

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Full text: https://www.imath.kiev.ua/~sigma/2020/009/
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Bibliographic databases:

ArXiv: 1909.13211
MSC: 35L67; 58K05; 32-04
Received: September 29, 2019; in final form February 18, 2020; Published online February 24, 2020
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Citation: Victor A. Vassiliev, “New Examples of Irreducible Local Diffusion of Hyperbolic PDE's”, SIGMA, 16 (2020), 009, 21 pp.

Citation in format AMSBIB
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\paper New Examples of Irreducible Local Diffusion of Hyperbolic PDE's
\jour SIGMA
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\vol 16
\papernumber 009
\totalpages 21
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