Vishal vasan

Vishal Vasan (born 1983) is an Indian mathematician.

Dr. Vasan studied mechanical engineering at the Anna University in Salem, Tamil Nadu where he received his baccalaureate degree in 2005. He then studied received his M.S. in Mechanical Engineering at Arizona State University in 2007 under the direction of Don L Boyer. Dr. Vasan earned his PhD in applied mathematics from the University of Washington in 2012 under the direction of Bernard Deconinck.

Dr. Vasan is currently at Pennsylvania State University Department of Mathematics as a post-doctoral fellow.

Work
Dr. Vasan works on boundary-value problems for integrable partial differential equations (PDEs) and water-waves and the tools required to study them. Integrable PDEs arise in many physical contexts including water-waves. However as integrable PDEs typically model only approximations to the water-wave equations, to completely understand the full equations one requires techniques from Potential theory and Bifurcation theory as well as numerical computations. The classical study of integrable systems is via the Inverse Scattering Transform. It turns out that boundary-value problems may be studied by suitably generalising this transform to what has become known as the Fokas Method. In fact, the Fokas method has a version for linear PDEs which helps in classifying well-posedness of boundary-value problems exactly. Recently, Dr. Vasan has become interested in inverse problems in the theory of water-waves, e.g. reconstruction of surface from pressure measurements, bathymetry detection from surface measurements, etc. The mathematics is related to the Fokas method, but with extra ingredients from potential theory since the waves are considered to be inviscid and irrotational.

Selected publications

 * The inverse water wave problem of bathymetry detection, J. Fluid Mechanics (submitted for publication) (2012) (with Bernard Deconinck)


 * Well-posedness of boundary-value problems for the linear Benjamin-Bona-Mahony equation, (submitted for publication) (2012) (with Bernard Deconinck)


 * Recovering the water-wave surface from pressure measurements (Accepted for the 10th International Conference on Mathematical and Numerical Aspects of Waves (Refereed Proceedings), WAVES 2011, Vancouver July 25–29, 2011) (with Diane Henderson, Katie Oliveras, and Bernard Deconinck)


 * Boundary-value problems for linear partial differential equations with mixed derivatives. (2011).  (with B. Deconinck)


 * Solving linear partial differential equations, SIAM Review, (2010). (with T. Trogdon and B. Deconinck)