Mathematics

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Grushin operators Project Report

Title: On a class of Grushin operators: a geometric mechanics approach We study a class of Grushin operators ¢G = @2 @x2 + x2k @2 @y2 ; k 2 N via the geometric mechanics approach, which is based on analysis of the

Quasilinear hyperbolic systems with dissipation effects

We study the Cauchy and the initial boundary value problems for a class of quasilinear hyperbolic systems with dissipation effects, such as frictional damping and relaxation. This kind of systems includes Euler equations as a special example. We aim to prove the

On Poicarés Uniformization Theorem

The study of Riemann surfaces begun in the 19th century when Riemann introduced them in his doctoral dissertation Foundations for a general theory of functions of a complex variable. An important perspective in the study of Riemann surfaces is the concept of

Algebraic Reconstruction Methods

Ill-posed sets of linear equations typically arise when discretizing certain types of integral transforms. A well known example is image reconstruction, which can be modeled using the Radon transform. After expanding the solution into a finite series of basis functions a large,