Existence and uniqueness of mass conserving solutions to the coagulation and collision-induced breakage equation

Das, Arijit; Saha, Jitraj

doi:10.1007/s41478-022-00407-z

Cited by 5 publications

(2 citation statements)

References 19 publications

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“…Paul & Kumar [22] established the existence and uniqueness theorem for pure collisional fragmentation equation. Recently, the existence and uniqueness of the solutions for the continuous collisional fragmentation equation with coagulation are studied by Das et al [23]. In [24,25], the weighted finite volume method (FVM) of Kumar et al [12] is extended to solve the univariate and bivariate nonlinear collisional breakage equations.…”

Section: (A) Literature Review and Motivationmentioning

confidence: 99%

Homotopy perturbation method and its convergence analysis for nonlinear collisional fragmentation equations

Yadav,

Das,

Singh

et al. 2023

Proc. R. Soc. A.

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The exploration of collisional fragmentation pheno-mena remains largely unexplored, yet it holds considerable importance in numerous engineering and physical processes. Given the nonlinear nature of the governing equation, only a limited number of analytical solutions for the number density function corresponding to empirical kernels are available in the literature. This article introduces a semi-analytical approach using the homotopy perturbation method to obtain series solutions for the nonlinear collisional fragmentation equation. The method presented here can be readily adapted to solve both linear and nonlinear integral equations, eliminating the need for domain discretization. To gain deeper insights intothe accuracy of the proposed method, a convergence analysis is conducted. This analysis employs the concept of contractive mapping within the Banach space, a well-established technique universally acknowledged for ensuring convergence. Various collisional kernels (product and polymerization kernels), breakage distribution functions (binary and multiple breakage) and various initial particle distributions are considered to obtain the new series solutions. The obtained results are successfully compared against finite volume method [26] solutions in terms of number density functions and their moments. The error between the exact and obtained series solutions is shown in plots and tables to confirm the applicability and accuracy of the proposed method.

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Section: (A) Literature Review and Motivationmentioning

confidence: 99%

Homotopy perturbation method and its convergence analysis for nonlinear collisional fragmentation equations

Yadav,

Das,

Singh

et al. 2023

Proc. R. Soc. A.

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“…Vigil et al [12] and Ke et al [13] provided the extensive analysis on coagulation with collision-induced fragmentation. Some other ex-istence and uniqueness studies can also be found in [14,15]. Various numerical approaches in 1D and 2D for solving these models have been discussed in detail by [16][17][18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

A Note on the Volume Conserving Solution to Simultaneous Aggregation and Collisional Breakage Equation

Kharchandy

Das

Thota

et al. 2023

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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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Approximate solutions to the nonlinear hyperbolic population balance equation: convergence, error estimate and numerical simulations

Das,

Saha

2024

Z. Angew. Math. Phys.

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Existence and uniqueness of mass conserving solutions to the coagulation and collision-induced breakage equation

Cited by 5 publications

References 19 publications

Homotopy perturbation method and its convergence analysis for nonlinear collisional fragmentation equations

Homotopy perturbation method and its convergence analysis for nonlinear collisional fragmentation equations

A Note on the Volume Conserving Solution to Simultaneous Aggregation and Collisional Breakage Equation

Approximate solutions to the nonlinear hyperbolic population balance equation: convergence, error estimate and numerical simulations

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