Wave phenomena are ubiquitous in nature. Their mathematical modeling, simulation and analysis lead to fascinating and challenging problems in both analysis and numerical mathematics. These challenges and their impact on significant applications have inspired major results and methods about wave-type equations in both fields of mathematics. The Conference on Mathematics of Wave Phenomena 2018 held in Karlsruhe, Germany, was devoted to these topics and attracted internationally renowned experts from a broad range of fields. These conference proceedings present new ideas, results, and techniques from this exciting research area.

Wave phenomena are ubiquitous in nature. Their mathematical modeling, simulation and analysis lead to fascinating and challenging problems in both analysis and numerical mathematics. These challenges and their impact on significant applications have inspired major results and methods about wave-type equations in both fields of mathematics. The Conference on Mathematics of Wave Phenomena 2018 held in Karlsruhe, Germany, was devoted to these topics and attracted internationally renowned experts from a broad range of fields. These conference proceedings present new ideas, results, and techniques from this exciting research area.

This book presents the notes from the seminar on wave phenomena given in 2019 at the Mathematical Research Center in Oberwolfach. The research on wave-type problems is a fascinating and emerging field in mathematical research with many challenging applications in sciences and engineering. Profound investigations on waves require a strong interaction of several mathematical disciplines including functional analysis, partial differential equations, mathematical modeling, mathematical physics, numerical analysis, and scientific computing. The goal of this book is to present a comprehensive introduction to the research on wave phenomena. Starting with basic models for acoustic, elastic, and electro-magnetic waves, topics such as the existence of solutions for linear and some nonlinear material laws, efficient discretizations and solution methods in space and time, and the application to inverse parameter identification problems are covered. The aim of this book is to intertwine analysis and numerical mathematics for wave-type problems promoting thus cooperative research projects in this field.

This book consists of five introductory contributions by leading mathematicians on the functional analytic treatment of evolutions equations. In particular the contributions deal with Markov semigroups, maximal L DEGREESp-regularity, optimal control problems for boundary and point control systems, parabolic moving boundary problems and parabolic nonautonomous evolution equations. The book is addressed to PhD students, young researchers and mathematicians doing research in one of the above topics.

Dieses Lehrbuch befasst sich mit mathematischen Modellen fur dynamische Prozesse aus den Biowissenschaften. Behandelt werden Dynamiken von Populationen, Epidemien, Viren, Prionen und Enzymen, sowie Selektion in der Genetik. Das Buch konzentriert sich auf Modelle, deren Formulierung auf gewoehnliche Differentialgleichungen fuhrt. Schwerpunkte der Kapitel sind sowohl die mathematische Modellierung als auch die Analyse der resultierenden Modelle, sowie die biologische beziehungsweise biochemische Interpretation der Ergebnisse. UEbungsaufgaben zu den Kapiteln erleichtern die Vertiefung des Stoffes. Das Buch schlagt eine Brucke zwischen elementaren Einfuhrungen in die Modellierung biologischer und biochemischer Systeme und mathematisch anspruchsvoller Spezialliteratur. Die vorgestellten Modelle und Techniken ermoeglichen Studenten und Dozenten aus den Bereichen Bioinformatik und Biomathematik den Einstieg in komplexere Themen und weiterfuhrende Literatur zur mathematischen Biologie. Der Text enthalt grundlegende, aber auch aktuelle Ergebnisse, die hier erstmals in Buchform erscheinen.