Global existence of solutions to the discrete Safronov-Dubovskiǐ coagulation equations and failure of mass-conservation

On the discrete Safronov–Dubovskiǐ coagulation equations: Well‐posedness, mass conservation, and asymptotic behavior

“…Kaushik and Kumar [26] establish the existence, uniqueness, and mass conservation of (1.3) and (1.4) when dealing with an unbounded kernel in the form of min{i, 𝑗}𝛾 i,𝑗 ≤ (i + 𝑗) for all i, 𝑗 ≥ 1 in the weighted l 1 space. In the same space, recently, in Ali and Giri [27], the existence of (1.3) and (1.4) is proved for the coagulation coefficients of a multiplicative type, which are defined as follows:…”

“…Kaushik and Kumar [26] establish the existence, uniqueness, and mass conservation of () and () when dealing with an unbounded kernel in the form of $$$ \min \left\{i,j\right\}{\gamma}_{i,j}\le \left(i+j\right) $$$ for all $$$ i,j\ge 1 $$$ in the weighted $$$ {l}_1 $$$ space. In the same space, recently, in Ali and Giri [27], the existence of () and () is proved for the coagulation coefficients of a multiplicative type, which are defined as follows: $$$$ {\gamma}_{i,j}={\theta}_i{\theta}_j+{\kappa}_{i,j}. $$$$ Moreover, these coefficients satisfy the following conditions: $$$$ \underset{i\ge 1}{\operatorname{inf}}\frac{\theta_i}{i}=B>0,\mathrm{and}\kern1.00em {\kappa}_{i,j}\le A{\theta}_i{\theta}_j\kern0.50em \mathrm{for}\ \mathrm{each}\kern0.50em i,j\ge 1\kern0.40em \left(A\ge 0\right).$$…”

On the discrete Safronov-Dubovskii coagulation equation: well-posedness, mass-conservation and asymptotic behaviour

“…In [19], the authors establishes the existence, uniqueness, and mass conservation of (1.3)-(1.4) when dealing with an unbounded kernel in the form of min{i, j}γ i,j ≤ (i + j) for all i, j ≥ 1 in the weighted l 1 space. In the same space, recently in [1], the existence of (1.3)-(1.4) is proved for the coagulation coefficients of a multiplicative type, which are defined as follows:…”