A Note on the Volume Conserving Solution to Simultaneous Aggregation and Collisional Breakage Equation
Farel William Viret Kharchandy,
Arijit Das,
Vamsinadh Thota,
Jitraj Saha,
Mehakpreet Singh
Affiliations
Farel William Viret Kharchandy
Department of Mathematics, National Institute of Technology Tiruchirappalli, Tamil Nadu 620015, India
Arijit Das
Department of Mathematics, National Institute of Technology Tiruchirappalli, Tamil Nadu 620015, India
Vamsinadh Thota
Department of Mathematics, National Institute of Technology Tiruchirappalli, Tamil Nadu 620015, India
Jitraj Saha
Department of Mathematics, National Institute of Technology Tiruchirappalli, Tamil Nadu 620015, India
Mehakpreet Singh
Mathematics Applications Consortium for Science and Industry (MACSI), Department of Mathematics and Statistics, University of Limerick, V94 T9PX Limerick, Ireland
A new population balance model is introduced, in which a pair of particles can coagulate into a larger one if their encounter is a completely inelastic collision; otherwise, one of them breaks into multiple fragments (two or more) due to the elastic collision. Mathematically, coagulation and breakage models both manifest nonlinearity behavior. We prove the global existence and uniqueness of the solution to this model for the compactly supported kinetic kernels and an unbounded breakage distribution function. A further investigation dealt with the volume conservation property (necessary condition) of the solution.
