Loughborough University is a top-ten rated university in England for research intensity (REF2014) and an outstanding 66% of the work of Loughborough’s academic staff who were eligible to be submitted to the REF was judged as ‘world-leading’ or ‘internationally excellent’, compared to a national average figure of 43%. 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 caLinear 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.reer.