A study of the collisional fragmentation problem using the Gamma distribution approximation

Existence of mass conserving solution for the coagulation–fragmentation equation with singular kernel

“…Over the years many researchers have studied the nonlinear behaviour of colisional fragmentation model, e.g., scaling solutions [14,18,23], shattering behaviour [1,25], existenceuniqueness and well-posedness of weak solution [26], Monte Carlo (Direct simulation) algorithm [27], discontinuous Galerkin scheme [28], etc. However, to the best of authors knowledge the existence-uniqueness result of a global mass preserving continuous solution for singular kernel collision rate is not studied yet.…”

An existence‐uniqueness result for the pure binary collisional breakage equation

“…Cheng and Redner mathematically developed the binary collisional breakage equation using the following integro‐differential equation: in accordance with the initial data, Without loss of any generality, the characteristics t and x are taken as dimensionless quantity . We recall that the collision kernel K ( x , y ) in illustrates the rate of successful collision for breakage between two particles of sizes x and y , respectively, while b ( x , y ; z ) is the breakage rate for formation of x size particle from y due to its impact with a z size particle . The collision kernel is symmetric in its arguments, i.e., As a concern, the breakage rate b ( x , y ; z ) is an extension of the general breakage rate involved in linear breakage plausible with an extra parameter z .…”

“…21 We recall that the collision kernel K(x, y) in (1) illustrates the rate of successful collision for breakage between two particles of sizes x and y, respectively, while b(x, y; z) is the breakage rate for formation of x size particle from y due to its impact with a z size particle. [20][21][22][23] The collision kernel is symmetric in its arguments, i.e.,…”

“…It is pertinent to mention that literature reveals most theoretical research works have comprised only with linear breakage and only few investigations have been presented to nonlinear breakage due to interactions between fragments, such as collision‐induced fragmentation . These circumstances are motivated the present study.…”

Comments on “A study of the collisional fragmentation problem using the gamma distribution approximation”

“…The recent paper by Kostoglou and Karabelas [1] studied the collisional fragmentation problem using an approximation based on the gamma distribution. The gamma approximation proposed in Section 2.5 of the paper involved computation of two types of integrals.…”