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Free Boundary Problems

Travelling waves in nonlinear diffusion-advection-reaction, 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 x0. Some examples of models (equations):

(porous media equation with convection, sources or sinks).

(non-Newtonian 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.


University of Rome 1
University of Tel-Aviv
University of Twente

For more information please contact

Róbert Kersner and Zsolt Biró. Room K427
Laboratory of Applied Mathematics Group of Mathematical Physics
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