Name
Abstract | ||
|---|---|---|
A mathematical model for collision-induced breakage is considered. Existence of weak solutions to the continuous nonlinear collision-induced breakage equation is shown for a large class of unbounded collision kernels and daughter distribution functions, assuming the collision kernel K to be given by K(x, y) = x(alpha) y(beta) + x(beta)y(alpha) with alpha <= beta <= 1. When alpha +beta is an element of [1, 2], it is shown that there exists at least one weak mass-conserving solution for all times. In contrast, when alpha + beta is an element of [0, 1) and alpha >= 0, global mass-conserving weak solutions do not exist, though such solutions are constructed on a finite time interval depending on the initial condition. The question of uniqueness is also considered. Finally, for alpha < 0 and a specific daughter distribution function, the nonexistence of mass-conserving solutions is also established. |
Year | DOI | Venue |
|---|---|---|
2021 | 10.1137/20M1386852 | SIAM JOURNAL ON MATHEMATICAL ANALYSIS |
Keywords | DocType | Volume |
collision-induced fragmentation, well-posedness, nonexistence, mass conservation | Journal | 53 |
Issue | ISSN | Citations |
4 | 0036-1410 | 0 |
PageRank | References | Authors |
0.34 | 0 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Ankik Kumar Giri | 1 | 1 | 1.06 |
| Philippe Laurençot | 2 | 30 | 10.30 |