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math.AP2025
Chemotaxis-consumption interaction: Solvability and asymptotics in general high-dimensional domains
Johannes Lankeit, Michael Winkler
The basic chemotaxis-consumption model \[ u_t = Îu - \nabla \cdot(u\nabla v),\qquad\qquad v_t = Îv - uv \] is considered in general, possibly non-convex bounded domains of arbitr…
math.AP2024
A model for heat generation by acoustic waves in piezoelectric materials: Global large-data solutions
Leander Claes, Johannes Lankeit, Michael Winkler
A model for the generation of heat due to mechanical losses during acoustic wave propagation in a solid is considered in a Kelvin-Voigt type framework. In contrast to previous stud…
math.AP2024
Global solvability of a model for tuberculosis granuloma formation
Mario Fuest, Johannes Lankeit, Masaaki Mizukami
We discuss a nonlinear system of partial differential equations modelling the formation of granuloma during tuberculosis infections and prove the global solvability of the homogene…