72 citations · 455 across the 28 of their papers we have counts for
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Chemotaxis(-fluid) systems with logarithmic sensitivity and slow consumption: global generalized solutions and eventual smoothness
Mario Fuest
We consider the system \begin{align*} \begin{cases} n_t + u \cdot \nabla n = Δn - χ\nabla \cdot (\frac{n}{c} \nabla c), \\ c_t + u \cdot \nabla c = Δc - nf(c), \\ u_t + (u \cdot \n…
Possible points of blow-up in chemotaxis systems with spatially heterogeneous logistic source
Tobias Black, Mario Fuest, Johannes Lankeit +1
We discuss the influence of possible spatial inhomogeneities in the coefficients of logistic source terms in parabolic-elliptic chemotaxis-growth systems of the form \begin{align*}…
Global existence of classical solutions and numerical simulations of a cancer invasion model
Mario Fuest, Shahin Heydari, Petr Knobloch +2
In this paper, we study a cancer invasion model both theoretically and numerically. The model is a nonstationary, nonlinear system of three coupled partial differential equations m…
Strong convergence of weighted gradients in parabolic equations and applications to global generalized solvability of cross-diffusive systems
Mario Fuest
In the first part of the present paper, we show that strong convergence of in and weak convergence of $(f_{\varepsilon})_{\v…