Applications to ODEs and PDEs

In a number of situations, and especially for the study of evolutionary partial differential equations (PDEs), it proves to be helpful to perform a partial Fourier transform, which do not involve all the variables, but only some of them. This process will be briefly described, using the framework of evolutionary problems, which is its main application. The heat equation is the partial differential equation. The wave equation is also the partial differential equation. This chapter presents applications to ordinary differential equations (ODEs) and PDEs. The partial Fourier transform is endowed of the same continuity and invertibility properties as the usual Fourier transform.