Analysis of diffuse and sharp interface models
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Organizer(s): |
Name:
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Affiliation:
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Country:
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Alain Miranville
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University of Poitiers
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France
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Andrea Giorgini
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Politecnico di Milano
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Italy
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Maurizio Grasselli
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Politecnico di Milano
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Italy
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Introduction:
| | Numerous significant real-world phenomena are characterized by the
evolution of interfaces separating distinct chemical species, such as
the behavior of multi-phase fluids, intracellular phase separation,
tumor growth dynamics, image reconstruction (inpainting), and
self-assembly processes in diblock copolymers.
The classical description of moving interfaces is called Sharp Interface (SI)
theory. The interface separating the phase boundary is assumed to be
an evolving in time surface with zero thickness. This formulation
leads to free-boundary problems. A more recent approach instead treats
the interface as a narrow region with finite thickness. This is the
so-called Diffuse Interface (DI) theory. In the latter case, the
evolution of the interface is described as the level set of the fluid
concentration (called phase-field), which is uniform in bulk phases
and varies steeply but continuously across the interface.
Over the past few decades, there has been remarkable activity in both the
theoretical analysis and numerical simulations of SI and DI models.
This session aims to spotlight recent advancements in these fields and
possibly related free boundary problems, providing a platform for
experts in the field and emerging researchers to share their
cutting-edge techniques, innovative perspectives, and future goals.
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