Nonlinear evolution operators and wavelets Original Research Article

Evolution operators and wavelets are very interesting and attractive, not only by their extremely wide range of applications, but also by their theories of great importance. It is very difficult to show the relations between evolution operators, wavelets and other subjects in pure and applied mathematics. However, perhaps taking into account the obvious relations between the microlocal and wavelet analysis and the white noise; the Brownian motion and the index formulae for de Rham complex; even only on archimedean fields, we can partially illustrate such interesting relations. In our brief talk, let us present some recent results on a semilinear non-classical evolution problem and a Galerkin-wavelet method to solve a very complicated linear evolution one. Then some general results on stationary problems, from which we can continue to study the respective non-stationary cases, will be introduced.