IU mathematician honored for best paper in partial differential equations

  • Dec. 9, 2015


BLOOMINGTON, Ind. -- IU mathematician Kevin Zumbrun was honored today for his work on partial differential equations by the Society for Industrial and Applied Mathematics.

The SIAM Applied Mathematics' Activity Group Award is awarded annually to the authors of the most outstanding paper on this subject published in English in a peer-reviewed journal in the past year. 

Zumbrun is a Distinguished Professor in the IU Bloomington College of Arts and Sciences' Department of Mathematics. The paper, "Behavior of periodic solutions of viscous conservation laws under localized and nonlocalized perturbations," appeared in the July 2014 print issue of the journal Inventiones Mathematicae.

The work provides new mathematical techniques for the study of Whitham modulation equations, a powerful tool used to predict wave modulation in signals such as radio transmissions. The results both definitively verify the accuracy of these equations and provide new physical information about the underlying waves.

"Kevin has made numerous insightful and deep contributions to the field of stability of traveling wave fronts," said Elizabeth Housworth, chair and professor in the IU Bloomington Department of Mathematics. "The SIAG-APDE prize recognizes his leadership and recent work with colleagues on the stability and asymptotic behavior of periodic traveling wave solutions for a large class of dissipative systems. The Department of Mathematics congratulates him on this well-deserved honor."

Zumbrun is a top mathematician in the field of nonlinear partial differential equations. His work in the area has opened up an entire school of thought on the subject.

His innovative approach to the determination of the stability of waves helped start a revolution in the approach to determining the stability of viscous shock waves. He has also solved long-standing and technically distinct open problems such as stability of Navier-Stokes shocks, multidimensional stability of viscous shock waves, behavior in the inviscid and strong shock limits, and dynamics and bifurcation of shock and boundary layers.

Zumbrun is also known is for solving, in collaboration with colleagues, the 35-year open problem of behavior of periodic Kuramoto-Sivashinsky waves, which had been previously regarded as intractable by existing theory.

In addition to the SIAM-APDE Prize, Zumbrun is the recipient of the 1994 Navy Young Investigator Award and the 2004 Dean’s Distinguished Research Fellowship from IU. He was also named a fellow of the American Mathematical Society and received the prestigious appointment Chaire d'Excellence de Paris in 2014.

A member of the IU faculty since 1992, Zumbrun served as chair of the IU Bloomington Department of Mathematics from 2009 to 2014. He holds a Ph.D. in mathematics from New York University and a master’s and bachelor's degree from the University of California, Davis. He is the author of over 150 publications and has received continuous support from the National Science Foundation since 1991.

Also winners of the award were paper co-authors Mathew A. Johnson of the University of Kansas; Pascal Noble of the University of Toulouse, France; and L. Miguel Rodrigues of the University of Lyon, France.

The honor was presented at the 2015 SIAM Conference on Analysis of Partial Differential Equations in Scottsdale, Ariz.

Kevin Zumbrun

Kevin Zumbrun | Photo by Indiana University

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