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.
Citation
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. https://doi.org/10.11650/tjm/171104
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