Products of distributions and collision of a δ-wave with a δ′-wave in a turbulent model

DOI

10.1080/14029251.2015.1079421How to use a DOI?

Keywords

Products of distributions; Collisions of δ-waves with δ′-waves; Delta-solitons; inviscid Burgers equation

Abstract

We study the possibility of collision of a δ-wave with a stationary δ′-wave in a model ruled by equation f (t)u_t+[u²−β(x−γ(t))u]_x = 0, where f, β and γ are given real functions and u = u(x, t) is the state variable. We adopt a solution concept which is a consistent extension of the classical solution concept. This concept is defined in the setting of a distributional product, which is not constructed by approximation processes. By a convenient choice of f, β and γ, we are able to distinguish three distinct dynamics for that collision, to which correspond phenomena of solitonic behaviour, scattering, and merging. Also, as a particular case, taking f = 2 and β = 0 we prove that the referred collision is impossible to arise in the setting of the inviscid Burgers equation. To show how this framework can be applied to other physical models, we included several results already obtained.

Copyright

© 2015 The Authors. Published by Atlantis Press and Taylor & Francis

Open Access

This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - C.O.R. Sarrico
AU  - A. Paiva
PY  - 2021
DA  - 2021/01/06
TI  - Products of distributions and collision of a δ-wave with a δ′-wave in a turbulent model
JO  - Journal of Nonlinear Mathematical Physics
SP  - 381
EP  - 394
VL  - 22
IS  - 3
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2015.1079421
DO  - 10.1080/14029251.2015.1079421
ID  - Sarrico2021
ER  -