Preface

This special issue of the journal Applicable Analysis contains a set of contributions based on talks delivered at the conference ‘Scaling Up and Modeling for Transport and Flow in Porous Media’ – http://web.math.hr/~jurak/Dubrovnik08/ – which was held in Dubrovnik, Croatia from October 13 to October 16, 2008. This conference was jointly organized by the Department of Mathematics of the University of Zagreb (Croatia), the Applied Mathematics Laboratory of the University of Pau & CNRS UMR 5142 (France), the Camille Jordan Institute of the University of Lyon & CNRS UMR 5208 (France), and the National Research Group MoMaS/CNRS PACEN (France). This conference was dedicated to our longtime friend and collaborator, Professor Alain Bourgeat, on the occasion of his 60th birthday.

The aim of the conference was to bring together researchers, scientists, engineers, and students to exchange and share their experiences, new ideas, and research results about upscaling for modelling, analysis and simulation of flow and transport in porous media and application to problems including subsurface hydrology, petroleum exploration, contaminant remediation, carbon sequestration and nuclear waste storage. This conference was attended by 75 participants from 15 different countries: Albania, Croatia, France, Germany, Israel, Italy, Morocco, The Netherlands, Norway, Russia, Slovakia, Tunisia, Ukraine, United Kingdom, and USA.

This special issue of the journal Applicable Analysis contains 11 contributions corresponding to a part of the 69 talks delivered at the conference. A complete list of the invited speakers is included. In selecting these papers, we followed the regular refereeing procedure. We would like to thank the authors for the effort in preparing their contributions and for meeting the deadlines. We would like to thank those whom we asked for their help in reviewing these papers. We also would like to thank the Editors-in-Chief of the journal Applicable Analysis for offering us the possibility to publish this special issue.

This special issue focus on Mathematical Modelling and Numerical Simulation of Flow and Transport in Porous Media. The contributions include work on a numerical method for waste repository problems with non standard interface condition; two asymptotic models for arrays of underground waste containers; on the homogenization of some double porosity models with periodic thin structures; parabolic H-convergence and small-amplitude homogenization; numerical modelling of multi-component multi-phase flows in petroleum reservoirs with heat transfer; a fully equivalent global pressure formulation for three phases compressible flows; boundary value problem in a cascade thick junction with a random transmission zone; twisting a thin periodically perforated elastic rod; upscaling of transport processes in porous media with biofilms in equilibrium and non-equilibrium conditions; scaling up through domain decomposition; existence of solutions for a model of multiphase flow in porous media.

List of Invited Speakers:

• Grégoire Allaire, Ecole Polytechnique, France

• Tod Arbogast, University of Texas at Austin, USA

• Gilles Bernard-Michel, CEA, France

• Jacques Blum, University of Nice, France

• Guy Bouchitté, University of Toulon & Var, France

• Guy Chavent, INRIA, France

• Gregory A. Chechkin, Moscow Lomonosov State University, Russia & Narvik University, Norway

• Robert P. Gilbert, University of Delaware, USA

• Jérôme Jaffré, INRIA, France

• Peter Knaber, University Erlangen-Nürnberg, Germany

• Roland Masson, IFP, France

• Andro Mikelić, University of Lyon, France

• François Murat, University Paris VI, France

• Grigory Panasenko, University of Saint-Etienne, France

• Mikhail Panfilov, LEMTA-ENSEM, France

• Leonid Pankratov, FTINT, Ukraine

• Andrey Piatnitski, Narvik University, Norway and Lebedev Physical Institute, Russia

• Olivier Pironneau, University of Paris VI, France

• Michel Quintard, IMFT, France

• Jean Roberts, INRIA, France

• Thomas F. Russell, National Science Foundation, USA

• Ralph E. Showalter, Oregon State University, USA

• Peppino Terpolilli, Total, France

• Damien Tromeur-Dervout, University of Lyon, France

• Mary F. Wheeler, University of Texas at Austin, USA

We would like to thank the members of the organizing committee for their active role in the organization. Last, but not least, we want to acknowledge all participants for their contribution and efforts in making the conference an interesting, pleasant and successful event.