Factorization of Boundary Value Problems Using the Invariant Embedding Method

Jacques Henry is Director of Research, emeritus at INRIA Bordeaux Sud-ouest, France. He graduated from E´cole Polytechnique, Paris (1970). He has worked within INRIA (National Institute for Computer Sciences and Automatic Control, France) since 1974. His work covers control of systems governed by partial differential equations, modeling, parameter estimation and continuation-bifurcation methods applied to biological systems mainly in cardiac electrophysiology and biological sequences comparison. His current interests are on numerical analysis, inverse problems and singular perturbations for partial differential equations. He is developing research on the method of factorization of linear elliptic boundary value problems in terms of product of Cauchy problems. He was leading the INRIA project team Anubis on structured population dynamics. He has a special interest on the evolution of activity of popula- tions of neurons. His research is focused on modeling, optimization and simulation in Science and Technology, mainly using Partial Differential Equations. His research lines are the following: Epidemic modeling, spatial-stochastic individual based models, SIR models, hybrid models, risk analysis, validation with real data, control measures, economic and climate change impact analysis. He received his PhD. in Applied Mathematics from UCM< in July 1996. He is Director of the UCM Research Group Mathematical Models in Science and Engineering: Development, Analysis, Numerical Simulation and Control (MOMAT) since 2005.

1: Presentation of the Formal Computation of Factorization

2: Justification of the Factorization Computation

3: Complements to the Model Problem

4: Interpretation of the Factorization through a Control Problem

5: Factorization of the Discretized Problem

6: Other Problems

7: Other Shapes of Domain

8: Factorization by the QR Method

9: Representation Formulas for Solutions of Riccati Equations