The principal investigator and his graduate students will develop and use asymptotic and numerical methods to study a number of problems in applied mathematics. In particular, they will study the scattering of sound waves by inhomogeneous structures, strong localized perturbations of eigenvalues, diffusion in bounded and unbounded shear flows, and the pairing of eigenvalues of the Laplace operator in certain planar domains. Many natural phenomena are described by differential equations whose solutions are difficult to find using traditional techniques of applied mathematics. The principal investigator and his graduate students will apply asymptotic and numerical methods of nonstandard types in order to approximate accurately the solutions of problems in diverse areas of applied mathematics such as acoustic scattering and nonlinear diffusion.
