Existence of Mass-Conserving Weak Solutions to the Continuous Smoluchowski Coagulation Equations

Abstract: In this talk, we discuss the existence of mass-conserving weak solutions to the continuous version Smoluchowski coagulation equation (SCE) [3] on a suitable weighted  L¹ space .  Here, the coagulation kernels featuring an algebraic singularity for small volumes and growing linearly for large volumes, thereby extending previous results obtained in Norris [2] and Cueto Camejo & Warnecke [1].   In particular, linear growth at infinity of the coagulation kernel is included and the initial condition may have an infinite second moment.  Moreover, we have shown all weak solutions (in a suitable sense) including the ones constructed herein are mass-conserving, a property which was proved in Norris (1999) under stronger assumptions.  The existence proof relies on a weak compactness method in L¹ and a by-product of the analysis is that both conservative and non-conservative approximations to the SCE lead to weak solutions which are then mass-conserving.