PhD Studentship: Hyperbolic Equations with Irregular Coefficients: Very Weak Solutions and Applications

Loughborough University

Application details:

Start date of studentship: 1st October 2018

Closing date for applications: 16th February 2018


Primary supervisor: Claudia Garetto

Secondary supervisor: Marco Discacciati

Loughborough University is a top-ten rated university in England for research intensity (REF2014). In choosing Loughborough for your research, you’ll work alongside academics who are leaders in their field. You will benefit from comprehensive support and guidance from our Doctoral College, including tailored careers advice, to help you succeed in your research and future career.

Find out more:

Full Project Detail:

Linear and nonlinear hyperbolic PDEs arise in basically all sciences (physics, chemistry, medicine, engineering, astronomy, etc.). In Physics, they model several important phenomena, from propagation of waves in a medium (for instance propagation of seismic waves during an earthquake) to refraction in crystals and gas-dynamics. This project is devoted to hyperbolic equations with irregular (distributional) coefficients and/or multiplicities. For such equations, it can be an issue to define what a solution is. For this reason, a notion of very weak solution based on the theoretical concept of approximation by regularisation has recently been introduced.  Promising and interesting results have been obtained for the wave equation supported by some numerical experiments. It is the purpose of this project to extend these results to a wider class of hyperbolic equations (m-order with irregular coefficients). This will be done first theoretically and then numerically on some specific examples.

Find out more:

Entry requirements:

Applicants should have, or expect to achieve, at least a 2:1 Honours degree (or equivalent) in Mathematics or a related subject. A relevant Master’s degree and/or experience in one or more of the following will be an advantage: Mathematics.

Funding information:

This studentship will be awarded on a competitive basis to applicants who have applied to this project and/or any of the advertised projects prioritised for funding by the School of Science.

The 3-year studentship provides a tax-free stipend of £14,553 (2017 rate) per annum (in line with the standard research council rates) for the duration of the studentship plus tuition fees at the UK/EU rate. International (non-EU) students may apply however the total value of the studentship will be used towards the cost of the International tuition fee in the first instance.

Contact details:

Name: Claudia Garetto

Email address:

Telephone number: 01509222870

How to apply:

All applications should be made online at Under programme name, select ‘Mathematical Sciences’.

Please quote reference number: CG/MA/2018

Share this PhD
  Share by Email   Print this job   More sharing options
We value your feedback on the quality of our adverts. If you have a comment to make about the overall quality of this advert, or its categorisation then please send us your feedback
Advert information

Type / Role:



Midlands of England