Professor Benoît Perthame is an outstanding mathematician, very well known for several landmark contributions to nonlinear partial differential equations. He also possesses the unusual characteristic that he is applying his great mathematical skills to mathematical modeling in biology and to the analysis of the resulting equations. This is a relatively recent field, which is now recognized as a prominent one, in which he began his works about thirty years ago.

Professor Perthame began to make first-class contributions to scalar conservation laws and various hyperbolic systems that can be reformulated in the phase space as kinetic equations. This approach provides a powerful tool for proving properties of the solutions, such as regularity in fractional Sobolev spaces or application of compensated compactness. One of his major results has been the proof of existence of global weak solutions including vacuum for isentropic gas dynamics.

During the 80's, together with F. Golse, R. Sentis and P.-L. Lions, Professor Perthame discovered various compactness lemmas of fundamental importance, which initiated the modern theory of kinetic equations. After that, he began to switch his interests to biology by formalizing new models for assemblies of neurons based on works by physicists (Brunel Hakim, Tao, Cai, Shelley, Rangan, etc.). Striking results of his include the justification of the blow-up for network models of Integrate-and-Fire neurons, and the analysis of the synchronization effect of the network, another fascinating issue.

Professor Perthame subsequently turned his interests to the fundamental issues of tissue growth and cancer therapy. The dominant view of living tissues is currently issued from mechanics and the cell division/death phenomenon complements a fluid mechanical description of the motion. The mathematical difficulties are due to the hyperbolic-parabolic structure of the systems, and the free boundaries. In this direction, he showed how various types of equations such as kinetic equations, abnormal diffusions, or flux-limited equations, can be used to model such systems.

Together with G. Barles, S. Mirrahimi, P. E. Souganidis, he developed a population theory for Darwin's evolution explaining how selection can be represented mathematically as solutions exhibiting Dirac concentrations in which dynamics occur on a long time scale.

Over the past decades, Professor Perthame has designed a new research program in the domain of Partial Differential Equations for Biology and Medicine. Besides new mathematical questions, this program has led to organize an INRIA team, first called BANG, now Musclees. As a result, mathematical biology has become a major research area within the Laboratoire Jacques-Louis Lions and more generally, in France, which now counts as a leading country in mathematical biology.

 

Major Honors, Awards and Recognitions

1. Grand Prize INRIA-French Academy of Sciences (2015)
2. Plenary Lecture, International Congress of Mathematicians (Seoul) (2014)
3. Blaise Pascal Award, European Academy of Sciences (2013)
4. Plenary Lecture, ICIAM Congress, Vancouver (2013)
5. R. Sacchi Landriani Prize, Accademia Lombarda (1997)
6. Silver Medal of the CNRS (1994)
7. Blaise Pascal Prize, French Academy of Sciences (1992)
8. Peccot Prize, College de France (1989)

 

Five Significant Scholarly Outputs

1. Parabolic Equations in Biology. Lecture Notes on Mathematical Modeling in the Life Sciences. Springer (2015).
2. Transport Equations in Biology. L. N. Birkhauser (2007).
3. Kinetic Formulation of Conservation Laws, Oxford Univ. Press (2002).
4. Advances in Kinetic Theory and Computing: Selected Papers, Series on Adv. in Math. for Applied Sc. 22. World Scientific, Singapour (1994), B. Perthame Editeur.
5. Kinetic Equations and Asymptotic Theory, Series in Applied Math. 4, Elsevier (2000), L. Desvillettes et B. Perthame Editeurs.