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This project proposal focuses on theoretical and computer analysis, and their mutual interplay, related to several classes of evolutionary models that have been recently designed to capture complex behavior of various fluid-like materials within the framework of nonlinear continuum mechanics. The characteristic keywords of these particular classes are implicit constitutive relations, nonlinear rate type fluids, nonlinear integral type fluid-like materials, inhomogeneous incompressible fluids, compressible non-Newtonian fluids, and chemically reacting fluids. Regarding specific applications, we intent to concentrate on unsteady flows of biological liquids and time-dependent processes in geophysical materials. The goal is to develop new methods and tools to solve initial boundary-value problems for large data, both theoretically and numerically.
IM leaders:
Participating institutions:
Institute of Mathematics, AS CR,
Faculty of Mechanical Engineering, Czech Technical University, FS ČVUT,
Mathematical Institute of Charles University, Prague , MU UK
