Taiwanese Journal of Mathematics

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

Carlos Orlando R. Sarrico

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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

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

Received: 21 February 2017
Revised: 15 November 2017
Accepted: 29 November 2017
First available in Project Euclid: 16 December 2017

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Mathematical Reviews number (MathSciNet)

Primary: 46F10: Operations with distributions 35D99: None of the above, but in this section 35L67: Shocks and singularities [See also 58Kxx, 76L05]

products of distributions conservation laws travelling shock waves travelling delta waves travelling waves which are not measures


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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