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Dynamical behaviour of a logarithmically sensitive chemotaxis model under time-dependent boundary conditions

European Journal of Applied Mathematics
This article studies the dynamical behaviour of classical solutions of a hyperbolic system of balance laws, derived from a chemotaxis model with logarithmic sensitivity, with time-dependent boundary conditions. It is shown that under suitable assumptions
Padi Fuster Aguilera, Kun Zhao
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Interpolation inequalities for weak solutions of nonlinear parabolic systems

Journal of Inequalities and Applications, 2011
The authors investigate differentiability of the solutions of nonlinear parabolic systems of order 2 m in divergence form of the following type ∑ | α | ≤ m ( - 1 ) | α | D α a α X , D u +
Floridia Giuseppe, Ragusa Maria
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Synchronized vector solutions for the nonlinear Hartree system with nonlocal interaction

Advanced Nonlinear Studies
We are concerned with the following nonlinear Hartree system−Δu+P1(|x|)u=α1|x|−1∗u2u+β|x|−1∗v2u inR3,−Δv+P2(|x|)v=α2|x|−1∗v2v+β|x|−1∗u2v inR3, $$\begin{cases}-{\Delta}u+{P}_{1}\left(\vert x\vert \right)u={\alpha }_{1}\left(\vert x{\vert }^{-1}\ast {u}^{2}
Gao Fashun, Yang Minbo, Zhao Shunneng
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Gradient estimates and Liouville-type theorems for a weighted nonlinear elliptic equation. [PDF]