TY - JOUR
T1 - Existence and Uniqueness of BV Solutions for a Class of Degenerate Boltzmann Equations with Measures as Initial Conditions
AU - Hongjun Yuan  & Yan Han 
JO - Journal of Partial Differential Equations
VL - 2
SP - 127
EP - 152
PY - 2009
DA - 2009/05
SN - 22
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5251.html
KW - System of discrete Boltzmann equations
KW - BV solutions
KW - existence and uniqueness
AB - <p>The existence and uniqueness of the solutions for the Boltzmann equations with measures as initial value are still an open problem which is posed by P. L. Lions (2000). The aim of this paper is to discuss the Cauchy problem of the system of discrete Boltzmann equations of the form ∂_tf_i+(f^{m_i}_i)_x=Q_i(f_1,f_2,...,f_n), (m_i &gt; 1, i=1,...,n) with non-negative finite Radon measures as initial conditions. In particular, the existence and uniqueness of BV solutions for the above problem are obtained.</p>