Department of Mathematics

Permanent URI for this community

http://nitt.ndl.gov.in/handle/123456789/43

Browse

Browsing Department of Mathematics by Author "Saha, Jitraj"

Now showing 1 - 3 of 3
  • No Thumbnail Available
    Item
    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.
  • No Thumbnail Available
    Item
    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.
  • No Thumbnail Available
    Item
    Conservative finite volume schemes for multidimensional fragmentation problems
    (MDPI AG, 2021-03-17) Saha, Jitraj; Bück, Andreas
    In this article, a new numerical scheme for the solution of the multidimensional fragmentation problem is presented. It is the first that uses the conservative form of the multidimensional problem. The idea to apply the finite volume scheme for solving one-dimensional linear fragmentation problems is extended over a generalized multidimensional setup. The derivation is given in detail for two-dimensional and three-dimensional problems; an outline for the extension to higher dimensions is also presented. Additionally, the existing one-dimensional finite volume scheme for solving conservative one-dimensional multi-fragmentation equation is extended to solve multidimensional problems. The accuracy and efficiency of both proposed schemes is analyzed for several test problems