Publication

Nonsmooth and nonenergetic solutions of PDE’s through convex integration

2022
Student project

Abstract

In this Master thesis we explore the convex integration method by S. Müller and V. Šverák and its applications to partial differential equations. In particular, we use it to build very irregular solutions to elliptic systems. We also apply this method to build very weak solutions to elliptic scalar-valued partial differential equations. For this, we also use staircase laminates invented by D. Faraco.

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Nonsmooth and nonenergetic solutions of PDE’s through convex integration

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Model reduction of coupled systems based on non-intrusive approximations of the boundary response maps

Fast global spectral methods for three-dimensional partial differential equations

Model reduction of coupled systems based on non-intrusive approximations of the boundary response maps

Fast global spectral methods for three-dimensional partial differential equations