Lyapunov functions and $L^{p}$-estimates for a class of reaction-diffusion systems

By Dirk Horstmann. 2001

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Prevention of blow-up by fast diffusion in chemotaxis (2010, background): “see [8,18]), it is then natural to study (multiple) steady state solutions of (1.”
Global Solutions of Some Chemotaxis and Angiogenesis Systems in High Space Dimensions (2004, background): “Let us just mention that system (2) has a conserved energy (see for example [9], [21] and [25]) given by d dt ∫ {”
PDE Models for Chemotactic Movements: Parabolic, Hyperbolic and Kinetic (2004, background): “Let us just mention that the system (1) has a conserved energy (see for example [10], [27] and [34]) given by _d dť / { n ( l n n - 1) - | | V c | 2 } dx = - / n | V ( l n n - Xc)\ 2 dx ^ 0.”
Global existence for chemotaxis with finite sampling radius (2006, unknown): “Horstmann [11]), self similar solutions (e.”
A user’s guide to PDE models for chemotaxis (2009, methodology): “Using Horstmann’s notation from [39], we need to find a solution R(u) of the differential equation”