Multidimensional asymptotic spectral analysis and applications

Abstract

This article addresses questions on localization and microlocalization in the framework of the so-called (𝒞, ℰ, 𝒫)-algebras of generalized functions. We give new results on nonlinear properties of the asymptotic singular spectrum in the multi-parameter case, a tool to describe the singularities of generalized solutions associated to problems which are classically ill-posed. We apply the theory to a transport equation with strongly irregular coefficients and initial data.

Keywords:

• algebras of generalized functions
• local and microlocal asymptotic analysis
• transport equation with irregular coefficients and irregular data

AMS Subject Classifications::

• 46F30
• 46T30
• 35D99