Studies properties and solutions of partial differential equations. Covers methods of characteristics, well-posedness, wave, heat and Laplace equations, Green's functions, and related integral ...

In this topic, our goal is to utilise and further develop the theory of non-linear PDEs to understand singular phenomena arising in geometry and in the description of the physical world. Particular ...

Multi-parameter Hardy spaces provide a refined framework for analysing functions and operators in settings where multiple scales or dimensions interact simultaneously. This theory extends the ...

Partial differential equations (PDE) describe the behavior of fluids, structures, heat transfer, wave propagation, and other physical phenomena of scientific and engineering interest. This course ...

Partial differential equations (PDEs) lie at the heart of many different fields of Mathematics and Physics: Complex Analysis, Minimal Surfaces, Kähler and Einstein Geometry, Geometric Flows, ...

A DIFFERENTIAL equation, in its usual form, states an analytical problem with a certain assumption as to the form of the answer. It implies the existence of a dependent variable, capable of being ...

Calculation: A representation of a network of electromagnetic waveguides (left) being used to solve Dirichlet boundary value problems. The coloured diagrams at right represent the normalized ...

Strict solutions u of genuinely nonlinear homogeneous hyperbolic equations in two independent variables with initial data f(x) of compact support become singular after a time interval of order |f|-1.

A wide variety of phenomena in science and engineering are mathematically modelled by partial differential equations (PDEs). This project aims to study asymptotic and control properties of special ...