Hyperbolic Problems: Theory, Numerics, Applications. Volume I

The present volume contains a selection of papers from the XVIII International Conference on Hyperbolic Problems: Theory, Numerics, and Applications (HYP2022), which was held on June 20-24, 2022 in Málaga (Spain). The goal of this series of conferences is to bring together scientists with interests in the theoretical, applied, and computational aspects of hyperbolic partial differential equations (systems of hyperbolic conservation laws, wave equations, etc.) and of related mathematical models. The chapters in this volume correspond to some of the plenary lectures and to selected contributions related to theoretical aspects.

Carlos M. Parés Madroñal is a full professor in Applied Mathematics at the University of Málaga, where he promoted the creation of the research group EDANYA. His research focuses on the numerical analysis of hyperbolic systems of partial differential equations with special emphasis on source terms and nonconservative products. He introduced the framework of path-conservative methods for the development of numerical methods with good properties such as well-balancing and high-order accuracy.

?Manuel J. Castro is a full professor in Applied Mathematics at the University of Málaga. His research focuses on the numerical analysis of hyperbolic PDEs and their applications to geophysical flows, as well as the design of innovative HPC numerical tools. He has contributed actively to the design of the HySEA software package, a high-performance software package for the simulation of geophysical flows, including tsunamis generated by earthquakes or landslides, river flooding, sediment transport and turbidity currents.

Tomás Morales de Luna is an associate professor at the University of Málaga and a member of the EDANYA group. His research focuses on modelling aspects of geophysical flows, with special interest in sediment transport and dispersive systems, and the design of robust and efficient finite volume schemes for hyperbolic systems of partial differential equations.

María Luz Muñoz Ruiz is an associate professor at the University of Málaga, where she is a member of the research group in Differential Equations, Numerical Analysis and Applications (EDANYA). This group focuses its research on the numerical simulation of geophysical flows through the numerical resolution of hydrodynamic models. Its interest is focused on the study of systems of nonconservative hyperbolic partial differential equations in general and shallow water equations in particular.