Revolutionary work in mathematics is awarded

December 06, 2007

Drs. Stefano Bianchini and Alberto Bressan will be honored for their breakthrough work in the analysis of partial differential equations, supplying new and powerful analytic ideas and establishing fundamental properties of the solutions.

Their paper, "Vanishing Viscosity Solutions of Nonlinear Hyperbolic Systems," (Annals of Mathematics, 161 (2005), 223-342) has been selected for the SIAM Activity Group on Analysis of Partial Differential Equations Prize. The award will be presented on December 11 at the biennial SIAM Conference on Analysis of Partial Differential Equations, held this year in Mesa, Arizona. Bianchini will accept the prize and present their paper at a plenary lecture entitled "Singular Approximations to Hyperbolic Systems of Conservation Laws."

Bianchini, of Italy's International School of Advanced Studies, and Bressan, of Pennsylvania State University, derived a solution to a problem that has remained unsolved for 50 years: the question of identifying hyperbolic systems as idealized limits of systems with low viscosity, or resistance to flow.

"They solved the outstanding problem in the field, that is, to find the limit of the solutions as the viscosity tends to zero," says Walter Strauss, Professor of Mathematics, Brown University. "They proved that the limit exists, is unique, and has finite total variation, at least if the initial variation is small. Their work has revolutionized this field of research."

Nonlinear hyperbolic systems of partial differential equations are associated with a wide range of physical phenomena, for example, the dynamics of unsteady fluid motions, liquid-vapor flows, the evolution of astrophysical bodies, motion of gravitational waves, and, in materials science, the dynamics of interfaces between solids.

It has long been believed - without proof until now - that viscosity affects the system only in the microstructure of the discontinuities and boundary layers, while the gross properties of the flow - far from shocks and boundaries - are unchanged by the details of how viscosity is modeled.

"Bianchini and Bressan have found an existence theorem that demonstrates how solutions to hyperbolic conservation laws can be realized as limits of viscous systems," says Barbara Lee Keyfitz, Professor of Mathematics at the University of Houston, and researcher in the field of nonlinear partial differential equations. "More important for the experts, they have been able to give a detailed analysis of how the wave structure actually evolves in the presence of viscosity. They are able to break a typical disturbance into its component parts, moving at different speeds, and to show that this evolution is independent of viscosity. It was the correct resolution of a wave into families--an idea that had eluded all researchers until now--that enabled this elegant result."

The SIAM Activity Group on Analysis of Partial Differential Equations (SIAG/APDE) Prize, established in 2005, is awarded to the author(s) of the most outstanding paper published in the preceding four years, as determined by the prize committee. Members of the selection committee for the 2007 award were: Mary Pugh, Chair, University of Toronto, Canada; Yann Brenier, University of Nice, France; Alice Chang, Princeton University; Bjorn Engquist, University of Texas at Austin; Robert Pego, Carnegie Mellon University.
The Society for Industrial and Applied Mathematics (SIAM) is an international community of over 11,000 individual members, including applied and computational mathematicians, computer scientists, and other scientists and engineers. The Society advances the fields of applied mathematics and computational science by publishing a series of premier journals and a variety of books, and producing a wide selection of conferences. More information about SIAM is available at

The SIAM Activity Group on Analysis of Partial Differential Equations fosters activity in the analysis of partial differential equations (PDE) and enhances communication between analysts, computational scientists and the broad PDE community. Its goals are to provide a forum where theoretical and applied researchers in the area can meet, to be an intellectual home for researchers in the analysis of PDE, to increase conference activity in PDE, and to enhance connections between SIAM and the mathematics community.

Society for Industrial and Applied Mathematics

Related Mathematics Articles from Brightsurf:

A new method for boosting the learning of mathematics
How can mathematics learning in primary school be facilitated? UNIGE has developed an intervention to promote the learning of math in school.

Could mathematics help to better treat cancer?
Impaired information processing may prevent cells from perceiving their environment correctly; they then start acting in an uncontrolled way and this can lead to the development of cancer.

People can see beauty in complex mathematics, study shows
Ordinary people see beauty in complex mathematical arguments in the same way they can appreciate a beautiful landscape painting or a piano sonata.

Improving geothermal HVAC systems with mathematics
Sustainable heating, ventilation, and air conditioning systems, such as those that harness low-enthalpy geothermal energy, are needed to reduce collective energy use and mitigate the continued effects of a warming climate.

How the power of mathematics can help assess lung function
Researchers at the University of Southampton have developed a new computational way of analyzing X-ray images of lungs, which could herald a breakthrough in the diagnosis and assessment of chronic obstructive pulmonary disease (COPD) and other lung diseases.

Mathematics pushes innovation in 4-D printing
New mathematical results will provide a potential breakthrough in the design and the fabrication of the next generation of morphable materials.

More democracy through mathematics
For democratic elections to be fair, voting districts must have similar sizes.

How to color a lizard: From biology to mathematics
Skin color patterns in animals arise from microscopic interactions among colored cells that obey equations discovered by Alan Turing.

US educators awarded for exemplary teaching in mathematics
Janet Heine Barnett, Caren Diefenderfer, and Tevian Dray were named the 2017 Deborah and Franklin Tepper Haimo Award winners by the Mathematical Association of America (MAA) for their teaching effectiveness and influence beyond their institutions.

Authors of year's best books in mathematics honored
Prizes for the year's best books in mathematics were awarded to Ian Stewart and Tim Chartier by the Mathematical Association of America (MAA) on Jan.

Read More: Mathematics News and Mathematics Current Events is a participant in the Amazon Services LLC Associates Program, an affiliate advertising program designed to provide a means for sites to earn advertising fees by advertising and linking to