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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.
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