Free boundary problems in accretive growth

Accretive growth is a fundamental mechanism in nature and technology. From coral reefs and seashells to glaciers, 3D-printed objects, and biological tissues, many systems evolve by progressively adding new material at their boundaries. Understanding these processes poses major scientific challenges: the shapes of the systems change over time in complex ways, and their evolution depends on interactions between geometry, physical effects, and environmental factors.

This project aims to advance the mathematical theory of accretive growth. On the one hand, it focuses on developing new methods from the calculus of variations, partial differential equations, and front-propagation theory that are relevant to growth problems. On the other hand, it targets three key applications: the rupture of atherosclerotic plaques, strain buildup in 3D printing, and the optimization of bioprinting strategies.

The activities will be carried out by a new team of young scientists in Vienna, in collaboration with international experts in mathematics, mechanics, and materials science.

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This project is financed by the with a budget of 432K € (grant number 10.55776/PAT1408325).