Open Access
June, 2018 Multiplication of Distributions and Travelling Wave Solutions for the Keyfitz-Kranzer System
Carlos Orlando R. Sarrico
Taiwanese J. Math. 22(3): 677-693 (June, 2018). DOI: 10.11650/tjm/171104


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.


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Carlos Orlando R. Sarrico. "Multiplication of Distributions and Travelling Wave Solutions for the Keyfitz-Kranzer System." Taiwanese J. Math. 22 (3) 677 - 693, June, 2018.


Received: 21 February 2017; Revised: 15 November 2017; Accepted: 29 November 2017; Published: June, 2018
First available in Project Euclid: 16 December 2017

zbMATH: 06965392
MathSciNet: MR3807332
Digital Object Identifier: 10.11650/tjm/171104

Primary: 35D99 , 35L67 , 46F10

Keywords: Conservation laws , Products of distributions , travelling delta waves , travelling shock waves , travelling waves which are not measures

Rights: Copyright © 2018 The Mathematical Society of the Republic of China

Vol.22 • No. 3 • June, 2018
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