## Taiwanese Journal of Mathematics

### Multiplication of Distributions and Travelling Wave Solutions for the Keyfitz-Kranzer System

Carlos Orlando R. Sarrico

#### Abstract

The present paper concerns the study of distributional travelling waves for the model problem $u_{t} + (u^{2}-v)_{x} = 0$, $v_{t} + (u^{3}/3-u)_{x} = 0$, also called the Keyfitz-Kranzer system. In the setting of a product of distributions, which is not defined by approximation processes, we are able to define a rigourous concept of a solution which extends the classical solution concept. As a consequence, we will establish necessary and sufficient conditions for the propagation of distributional profiles and explicit examples are given. A survey of the main ideas and formulas for multiplying distributions is also provided.

#### Article information

Source
Taiwanese J. Math., Volume 22, Number 3 (2018), 677-693.

Dates
Revised: 15 November 2017
Accepted: 29 November 2017
First available in Project Euclid: 16 December 2017

https://projecteuclid.org/euclid.twjm/1513393252

Digital Object Identifier
doi:10.11650/tjm/171104

Mathematical Reviews number (MathSciNet)
MR3807332

#### Citation

Sarrico, Carlos Orlando R. Multiplication of Distributions and Travelling Wave Solutions for the Keyfitz-Kranzer System. Taiwanese J. Math. 22 (2018), no. 3, 677--693. doi:10.11650/tjm/171104. https://projecteuclid.org/euclid.twjm/1513393252

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