Condensation phenomena in nonlinear drift equations (Q2807095)

The authors study non-negative measure solutions of the nonlinear drift-type equation NEWLINE\[NEWLINE \partial_\tau f+\nabla_v\cdot(vf(1+f^\gamma)), \quad \gamma>0. NEWLINE\]NEWLINE In the case of one space variable they establish existence and uniqueness of measure solutions to the Cauchy problem. It is also demonstrated that solutions blow up in finite time and that the condensation of mass appears. Moreover, it is shown that in the limit as \(t\to\infty\) all the mass is eventually concentrated in the origin.