Manuscript Topics

Many-body wave scattering has long history. However, the results are very scarce in the cases when multiple scattering is of prime importance. Such results are of special interest for this special issue. Inverse problems are of interest both theoretically and practically. Most of the results on inverse scattering deal with over-determined data. It is of special interest the results in the cases when the data are not over-determined. The Navier-Stokes equations were more than 200 years in existence. One of the millennium problems asks whether the solution to these equations in R^3 exist for all times and is smooth provided that the data are smooth and properly decaying. For simplicity one can treat the motion of incompressible viscous fluid in the whole space R^3 without boundaries.

It is of interest to have results on global stability of solutions to nonlinear equations. The classical results by A. M. Lyapunov deal with ordinary nonlinear equations and stated in terms of the spectral properties of the linearized equations or in terms of the Lyapunov functions. it is of interest to expand Lyapunov's results and to use other approaches.

This special issue in Mathematical Physics deal with the topics:
many-body wave scattering;
inverse scattering problems;
inverse problems;
the Navier-Stokes problem;
stability of solutions to nonlinear problems;
creating materials with a desired refraction coefficient.

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