An application of semigroup theory to the pure fragmentation equation
Tóm tắt
The present work deals with the mathematical analysis of the population balance equation involving pure fragmentation using the semigroup theory of linear operators. The existence and uniqueness of non-negative, strong solution is established.
Tài liệu tham khảo
Edwards, B.F., M. Cai, and H. Han. 1990. Rate equation and scaling for fragmentation with mass loss. Physical Review A 41(10):5755.
Aizenman, M., and T.A. Bak. 1979. Convergence to equilibrium in a system of reacting polymers. Communications in Mathematical Physics 65(3):203–230.
Melzak, Z. 1957. A scalar transport equation. Transactions of American Mathematical Society 85(2):547–560.
Stewart, I.W. 1989. A global existence theorem for the general coagulation-fragmentation equation with unbounded kernels. Mathematical Methods in the Applied Sciences 11(5):627–648.
Stewart, I.W. 1990. A uniqueness theorem for the coagulation-fragmentation equation. Mathematical Proceedings of the Cambridge Philosophical Society 107:573–578.
McLaughlin, D.J., W. Lamb, and A. McBride. 1997. A semigroup approach to fragmentation models. SIAM Journal on Mathematical Analysis 28(5):1158–1172.
McGrady, E., and R.M. Ziff. 1987. Shattering transition in fragmentation. Physical review letters 58(9):892.
Ziff, R.M., and E. McGrady. 1985. The kinetics of cluster fragmentation and depolymerisation. Journal of Physics A: Mathematical and General 18(15):3027.
Ziff, R.M., and E. McGrady. 1986. Kinetics of polymer degradation. Macromolecules 19(10):2513–2519.
Giri, A.K., P. Laurencot, and G. Warnecke. 2012. Weak solutions to the continuous coagulation equation with multiple fragmentation. Nonlinear Analysis: Theory, Methods & Applications 75(4):2199–2208.
Pazy, A. 2012. Semigroups of linear operators and applications to partial differential equations, Vol. 44. Springer Science & Business Media.
Pryce, J.D. 2014. Basic methods of linear functional analysis, Courier Corporation.
Hille, E., Phillips, R.S. 1996. Functional analysis and semi-groups, Vol. 31. American Mathematical Society.