A paper entitled “on the Optimality of the Observability Inequalities for Parabolic and Hyperbolic Systems with Potentials” authored by Prof. Zhang Xu (with Dr. Thomas Duyckaerts and Prof. Enrique Zuazua) has been judged the Best Paper published in Ann. I. H. Poincaré–AN in 2008. Prof. Zhang Xu is the first Chinese expert to won this award.

In this paper, they proved the optimality of the observability inequality for both parabolic and hyperbolic systems with potentials in even space dimensions n≥2. They also gave a similar but weaker optimality result in odd space-dimensions. Meanwhile, problems related to the impact of the growth rates of the nonlinearities on the controllability of semi linear parabolic and hyperbolic equations were addressed in this paper. 

Prof. Zhang Xu was elected into “CAS (Chinese Academy of Sciences) Hundred Talents Program” in 2006.His research interests covers the distributed parameter control system, partial differential equations, stochastic control and so on. He has served as the associate editor of SIAM Journal on Control and Optimization and is currently the corresponding editor of ESAIM: Control, Optimization and Calculus of Variations. Besides, he was invited to give a 45-minute talk at the International Congress of Mathematicians in 2010.

The Nonlinear Analysis section of the Annales de l'Institut Henri Poincaré is an international journal created in 1983. It publishes original and high quality research articles on all domains concerned with nonlinear analysis, especially applicable to partial differential equations, mechanics, physics, economy, without overlooking the numerical aspects. The Best Paper Award is judged biyearly, one paper for one year.