Analysis and numerical solutions of fragmentation equation with transport.

Abstract

Fragmentation equations occur naturally in many real world problems, see [ZM85, ZM86, HEL91,

CEH91, HGEL96, SLLM00, Ban02, BL03, Ban04, BA06] and references therein. Mathematical

study of these equations is mostly concentrated on building existence and uniqueness theories

and on qualitative analysis of solutions (shattering), some effort has be done in finding solutions

analytically. In this project, we deal with numerical analysis of fragmentation equation with

transport. First, we provide some existence results in Banach and Hilbert settings, then we turn

to numerical analysis. For this approximation and interpolation theory for generalized Laguerre

functions is derived. Using these results we formulate Laguerre pseudospectral method and

provide its stability and convergence analysis. The project is concluded with several numerical

experiments.