
 

Free Boundary Problems Travelling waves in nonlinear diffusionadvectionreaction, transmission lines and in branching random walk
Free boundary problems (FBP) constitute (mathematical, biological, physical, etc.) research subject characterized by the occurence of frontiers whose locations are a priori unknown. These boundaries separate geometric regions with different properties. FBP arise mainly in boundary value problems of partial differencial equations. A travelling wave (TW) is a function of the form u = u(x  ct), c is the speed. It is called finite if u = 0 for x  ct ³ x_{0}. Some examples of models (equations): (porous media equation with convection, sources or sinks).
(nonNewtonian fluids in turbulent regime) (generalized telegraph equation, correlated random walk equation) In a given model a free boundary exists if and only if the equation, has a finite travelling ware solution. The search of these solutions can be reduced to the study of a singular nonlinear integral equation whose solutions must satisfy certain constraints. Partners University of Rome 1 For more information please contact Róbert Kersner and Zsolt Biró. Room K427  