Analytical solutions to fragmentation equations with flow

Global strict solutions to continuous coagulation-fragmentation equations with strong fragmentation

In this paper we give an elementary proof of the unique, global-in-time solvability of the coagulation-(multiple) fragmentation equation with polynomially bounded fragmentation and particle production rates and a bounded coagulation rate. The proof relies on a new result concerning domain invariance for the fragmentation semigroup which is based on a simple monotonicity argument.

Existence and Uniqueness of Density Conserving Solutions to the Coagulation-Fragmentation Equations With Strong Fragmentation

Using Burnett Equations to Derive an Analytical Solution to Pressure-Driven Gas Flow and Heat Transfer in Micro-Couette Flow

The aim of the present study is deriving an analytical solution to incompressible thermal flow in a micro-Couette geometry in the presence of a pressure gradient using Burnett equations with first- and second-order slip boundary conditions. The lower plate of the micro-Couette structure is stationary, whereas the upper plate moves at a constant velocity. Non-dimensional axial velocity and tempe...

Asymptotic Behaviour of Solutions to the Coagulation - Fragmentation Equations

Analytical Solutions of Exact Renormalization Group Equations

We study exact renormalization group equations in the framework of the effective average action. We present analytical solutions for the scale dependence of the potential in a variety of models. These solutions display a rich spectrum of physical behaviour such as fixed points governing the universal behaviour near second order phase transitions, critical exponents, first order transitions (som...