Products of distributions, conservation laws and the propagation of \(\delta'\)-shock waves (Q692756)

The paper first surveys a notion, proposed by the author, of product of certain distributions, then, with a definition of solution based on this distributional product, studies the propagation of singular travelling waves for conservation laws equations \(u_{t}+\left[ \phi (u)\right] _{x}=\psi (u),\)\ where \(\phi \)\ and \(\psi \)\ are entire functions. Conditions for\ the propagation of wave profiles \( \beta +m\delta \)\ and \(\beta +m\delta ^{\prime }\) are presented as well.