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Hyperbolic equations with irregular coefficients: very weak solutions and applications


Project Description

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, often it is already an issue to define what a solution is. For this reason, it has been recently introduced a notion of very weak solution based on the theoretical concept of approximation by regularisation. 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.

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: http://www.lboro.ac.uk/study/postgraduate/supporting-you/research/
Further information regarding the Department of Mathematical Sciences: https://www.lboro.ac.uk/departments/maths/research/

Full Project Detail

For further information see –
http://www.lboro.ac.uk/science/study/postgraduate-research/studentships/

Find out more

http://www.lboro.ac.uk/departments/maths/staff/academic/claudia-garetto/

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.

How to apply

All applications should be made online at http://www.lboro.ac.uk/study/apply/research/. Under programme name, select Mathematical Sciences.

Please quote reference number: CG/MA/2019.

Funding Notes

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 £14,777 (2018 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.

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