Direct and Inverse Problems with Applications

Mariana Chatzakou is a postdoctoral researcher at Ghent University, Belgium. Michael Ruzhansky is a senior full professor of Mathematics at Ghent University in Belgium, and a professor of Mathematics at Queen Mary University of London in the United Kingdom. Karel Van Bockstal is a postdoctoral researcher at Ghent University, Belgium.

• Fourier algebras and homomorphisms.- Dispersion phenomena and applications to evolution equations.- Subriemannian geometry and analysis of hypoelliptic PDE.- Stability results for Sobolev, logarithmic Sobolev, and related inequalities.- Semiconcavity, viscosity solutions and the square distance in Carnot groups.- Direct and inverse nonstationary scattering problems for Dirac-type system.- Quantitative homogenisation for differential equations with highly anisotropic partially degenerating coefficients.- Rigidity results for evolution PDEs on homogeneuos Lie groups.- An overview of dualities in non-commutative harmonic analysis.- Colombeau type extensions, assymptotic scales.- Analytical solutions to the Laplace equation on a hemispherical domain.- Uniform spectral asymptotics for high-contrast periodic media.- Asymptotic mean value formulas for the 𝑝-Laplacian in the Euclidean space and in the Heisenberg Group.- Global solutions for a class of nonlinear evolution equations in supercritical spaces.- An index transform method for solutions of the boundary value problems in a wedge.