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A broad range of phenomena in science and technology can be described by non-linear partial differential equations characterized by systems of conservation laws with source terms. Well known examples are hyperbolic systems with source terms, kinetic equations, and convection-reaction-diffusion equations. This book collects research advances in numerical methods for hyperbolic balance laws and kinetic equations together with related modelling aspects. All the contributions are based on the talks of the speakers of the Young Researchers’ Conference “Numerical Aspects of Hyperbolic Balance Laws and Related Problems”, hosted at the University of Verona, Italy, in December 2021.

Computer science—Mathematics. --- Mathematics—Data processing. --- Neural networks (Computer science). --- Mathematical Applications in Computer Science. --- Computational Mathematics and Numerical Analysis. --- Mathematical Models of Cognitive Processes and Neural Networks. --- Artificial neural networks --- Nets, Neural (Computer science) --- Networks, Neural (Computer science) --- Neural nets (Computer science) --- Artificial intelligence --- Natural computation --- Soft computing --- Equacions diferencials no lineals --- Equacions en derivades parcials --- Solucions numèriques --- Neural networks (Computer science)

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In recent decades, kinetic theory - originally developed as a field of mathematical physics - has emerged as one of the most prominent fields of modern mathematics. In recent years, there has been an explosion of applications of kinetic theory to other areas of research, such as biology and social sciences. This book collects lecture notes and recent advances in the field of kinetic theory of lecturers and speakers of the School "Trails in Kinetic Theory: Foundational Aspects and Numerical Methods", hosted at Hausdorff Institute for Mathematics (HIM) of Bonn, Germany, 2019, during the Junior Trimester Program "Kinetic Theory". Focusing on fundamental questions in both theoretical and numerical aspects, it also presents a broad view of related problems in socioeconomic sciences, pedestrian dynamics and traffic flow management.

Numerical analysis --- Mathematics --- Mathematical physics --- Planning (firm) --- mathematische modellen --- wiskunde --- fysica --- numerieke analyse