Fitting parameters of a Fokker-Planck-like equation with constraint [PDF]
arXivWe analyse a Fokker-Planck like equation, driven by a scalar parameter in order to reach an integral constraint. We exhibit criteria guaranteeing existence-uniqueness of a solution. We also provide counter-examples. This problem is motivated by an application to the immune control of tumor growth.
arxiv
Mathematical models of neuronal growth. [PDF]
Biomech Model Mechanobiol, 2022 Oliveri H, Goriely A.
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Chemotaxis-consumption interaction: Solvability and asymptotics in general high-dimensional domains [PDF]
arXivThe basic chemotaxis-consumption model \[ u_t = \Delta u - \nabla \cdot(u\nabla v),\qquad\qquad v_t = \Delta v - uv \] is considered in general, possibly non-convex bounded domains of arbitrary spatial dimension. Global existence of weak solutions is shown, along with eventual smoothness of solutions and their stabilization in the large time limit.
arxiv
Nonlocal and local models for taxis in cell migration: a rigorous limit procedure. [PDF]
J Math Biol, 2020 Eckardt M +3 more
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Modelling chase-and-run migration in heterogeneous populations. [PDF]
J Math Biol, 2020 Colombi A +3 more
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Mathematical modelling of cell migration: stiffness dependent jump rates result in durotaxis. [PDF]
J Math Biol, 2019 Malik AA, Gerlee P.
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Aggregation-diffusion in heterogeneous environments. [PDF]
J Math BiolPotts JR.
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Well-posedness of Keller-Segel systems on compact metric graphs. [PDF]
J Evol EquShemtaga H, Shen W, Sukhtaiev S.
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An additive-noise approximation to Keller-Segel-Dean-Kawasaki dynamics: local well-posedness of paracontrolled solutions. [PDF]
Stoch Partial Differ EquMartini A, Mayorcas A.
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Modelling non-local cell-cell adhesion: a multiscale approach. [PDF]
J Math BiolZhigun A, Rajendran ML.
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