Browsing by Author "Das, Arijit"

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    A Note on the Volume Conserving Solution to Simultaneous Aggregation and Collisional Breakage Equation
    (MDPI, 2023-02-09) Kharchandy, Farel William Viret; Das, Arijit; Thota, Vamsinadh; Saha, Jitraj; Singh, Mehakpreet
    Abstract 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.
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    An application of semigroup theory to the coagulation-fragmentation models
    (TUBITAK, 2021-08-25) Das, Arijit; Das, Nilima; Saha, Jitraj
    We present the existence and uniqueness of strong solutions for the continuous coagulation-fragmentation equation with singular fragmentation and essentially bounded coagulation kernel using semigroup theory of operators. Initially, we reformulate the coupled coagulation-fragmentation problem into the semilinear abstract Cauchy problem (ACP) and consider it as the nonlinear perturbation of the linear fragmentation operator. The existence of the substochastic semigroup is proved for the pure fragmentation equation. Using the substochastic semigroup and some related results for the pure fragmentation equation, we prove the existence of global nonnegative, strong solution for the coagulation-fragmentation equation.