July 22, 2013

CIMPA Research School Evolutionary equations with applications in natural science


African Institute for Mathematical Sciences, Muizenberg, South Africa, 22 July–2 August 2013


The School is to take place at the African Institute of Mathematical Sciences (which recently signed the MOU with CIMPA) and will be a part of initiatives of the Mathematics for the Planet Earth year.

As the demand for accuracy of modelling phenomena occurring in the natural environment increases, so is the need for development of sophisticated mathematical techniques to analyse them. In particular, realistic models must be time dependent which naturally leads to evolutionary equations which balance changes in time with processes occurring in the state space which are modelled by partial, integral or integro-differential equations. Particular examples of such models are given by reaction-diffusion equations, transport equations coupled with Boltzmann type models or fragmentation-coagulation type equations. A common feature of these models is that they can be cast out in the form of ordinary differential equations posed in appropriate abstract state spaces and can be analysed within the framework of the theory of operator semigroups or infinite dimensional dynamical systems. The School is supposed to cover both theoretical background such as the functional analytic techniques (Sobolev spaces, elliptic PDEs, linear and nonlinear semigroups, time asymptotics and multiple scale phenomena) with applications to concrete models such as structured population models, reaction-diffusion equations with applications to ecological modelling, kinetic models such as fragmentation-coagulation equations or nonlocal epidemiological models, and transport and diffusion in networks. We also plan to partly cover approximate and numerical aspects of analysis of the models.


  • M. Mokhtar-Kharroubi (University of French-Comté, France), Spectral theory and time asymptotic analysis in kinetic theory
  • M. Sango (University of Pretoria, SA), Stochastic Partial Differential Equations in Fluid Dynamics
  • W. Lamb (University of Strathclyde, UK), Applying functional analytic techniques to evolution equations
  • P. Laurençot (University of Toulouse, France), Weak compactness techniques for coagulation equations
  • M. Banda (University of Stellenbosch, SA), Nonlinear Hyperbolic Systems of Conservation Laws and Related Applications
  • A. Marciniak-Czochra (University of Heidelberg, Germany), Reaction-diffusion equations and their applications to biological pattern formation
  • A. Bobrowski (Technical University of Lublin, Poland), Boundary conditions in evolutionary equations in biology
  • R. Rudnicki (Silesian University, Poland), Stochastic semigroups and their applications in physics and biology
  • E. Estrada (University of Strathclyde, UK), Dynamical and Evolutionary Processes on Complex Networks