@ARTICLE{10.21494/ISTE.OP.2020.0580,
TITLE={Initial value problem for the nonconservative zero-pressure gas dynamics system},
AUTHOR={Abhishek Das, K. T. Joseph, Manas R. Sahoo, },
JOURNAL={Advances in Pure and Applied Mathematics},
VOLUME={12},
NUMBER={Issue 1 (January 2021)},
YEAR={2021},
URL={http://www.openscience.fr/Initial-value-problem-for-the-nonconservative-zero-pressure-gas-dynamics-system},
DOI={10.21494/ISTE.OP.2020.0580},
ISSN={1869-6090},
ABSTRACT={In this article, we study initial value problem for the zero-pressure gas dynamics system in non conservative form and the associated adhesion approximation. We use adhesion approximation and modi-ed adhesion approximation in the construction of weak asymptotic solution. First we prove a general existence result for the adhesion model for the initial velocity component in $$$H^s \mbox{ for } s$$$ > $$$ \frac{n}{2} + 1$$$ and the initial data for the density component being a $$$C^1$$$ function. Using this, we construct weak asymptotic solution for the system with initial velocity in $$$L^2 \cap L^{\infty}$$$ and the initial density being a bounded Borel measure. Then we make a detailed analysis of the explicit formula for the weak asymptotic solution and generalized solution for the plane-wave type initial data.}}