This article surveys the mathematical aspects of traveling waves of a class of chemotaxis
models with logarithmic sensitivity, which describe a variety of biological or medical …

In this paper, we are concerned with a quasi-linear hyperbolic-parabolic system of
persistence and endogenous chemotaxis modelling vasculogenesis. Under some suitable …

The asymptotic behavior of solutions to a singular chemotaxis system modeling the onset of
tumor angiogenesis in two and three dimensional whole spaces is investigated in the paper …

The chemotaxis system {ut= Δ u−∇⋅(uv∇ v), vt= Δ v− uv,(⋆) is considered under
homogeneous Neumann boundary conditions in the ball Ω= BR (0)⊂ R n, where R> 0 and …

This paper establishes the nonlinear stability of traveling wave solutions to a chemotaxis
model with singular (or logarithmic) sensitivity and its transformed parabolic–hyperbolic …

In this paper, we establish the existence and the nonlinear stability of traveling wave
solutions to a system of conservation laws which is transformed, by a change of variable …

We consider the chemotaxis system ut= Δ u−∇⋅ uv∇ v,<? A3B2 [rowsep= 6pt]?> vt= Δ v−
uv, as originally introduced in 1971 by Keller and Segel in the second of their seminal works …

The Keller-Segel system has been widely proposed as a model for bacterial waves driven
by chemotactic processes. Current experiments on Escherichia coli have shown the precise …

We establish selection of critical pulled fronts in invasion processes as predicted by the
marginal stability conjecture. Our result shows convergence to a pulled front with a …

This paper is devoted to the analytical study of initial–boundary value problems for a system
of hyperbolic balance laws derived from a repulsive chemotaxis model with logarithmic …