STOCHASTIC FRAGMENTATION AND SOME SUFFICIENT CONDITIONS FOR SHATTERING TRANSITION Jeon, In-Tae;
We investigate the fragmentation process developed by Kolmogorov and Filippov, which has been studied extensively by many physicists (independently for some time). One of the most interesting phenomena is the shattering (or disintegration of mass) transition which is considered a counterpart of the well known gelation phenomenon in the coagulation process. Though no masses are subtracted from the system during the break-up process, the total mass decreases in finite time. The occurrence of shattering transition is explained as due to the decomposition of the mass into an infinite number of particles of zero mass. It is known only that shattering phenomena occur for some special types of break-up rates. In this paper, by considering the n-particle system of stochastic fragmentation processes, we find general conditions of the rates which guarantee the occurrence of the shattering transition.
Different aspects of a random fragmentation model, Stochastic Processes and their Applications, 2006, 116, 3, 345
On conservativity and shattering for an equation of phytoplankton dynamics, Comptes Rendus Biologies, 2004, 327, 11, 1025
ENDOGENOUS DOWNWARD JUMP DIFFUSION AND BLOW UP PHENOMENA BEFORE CRASH, Bulletin of the Korean Mathematical Society, 2010, 47, 6, 1105
Loss of mass in deterministic and random fragmentations, Stochastic Processes and their Applications, 2003, 106, 2, 245
Strictly substochastic semigroups with application to conservative and shattering solutions to fragmentation equations with mass loss, Journal of Mathematical Analysis and Applications, 2004, 293, 2, 693
Shattering and non-uniqueness in fragmentation models—an analytic approach, Physica D: Nonlinear Phenomena, 2006, 222, 1-2, 63
Comm. Math. Phys., 1979.
Comm. Math. Phys., 1986.
Probab. Theory Related Fields, 2000.
Phys. Rev. E., 1998.
Phys. Rev. Lett., 1988.
J. Theoret. Probab., 1999.
Phys. Rev. A., 1990.
Theory Probab. Appl., 1961.
Comm. Math. Phys., 1998.
J. Statist. Phys., 1999.