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Some remarks on well-posedness of the higher-dimensional chemorepulsion system

Cieślak Tomasz, Fujie Kentarou

Bulletin of the Polish Academy of Sciences. Mathematics

2019

Vol. 67, no. 2

165--178

We consider a fully parabolic system of chemorepulsion in higher dimensions. We introduce a new energy-like identity and comment on its relation to the Li-Yau-Hamilton inequalities. Next, we show that for the chemorepellent moving much more slowly than the cells, the time global well-posedness holds.

Some stability conditions for scalar Volterra difference equations

Berezansky L., Migda M., Schmeidel E.

Opuscula Mathematica

2016

Vol. 36, no. 4

459--470

New explicit stability results are obtained for the following scalar linear difference equation [formula] and for some nonlinear Volterra difference equations.

Of neutral type hyperbolic integrodifferential equation

Pachpatte B. G.

Fasciculi Mathematici

2008

Nr 40

57-69

In this paper we study the existence, uniqueness and other properties of solutions of a certain neutral type hyperbolic integrodifferential equation in two independent variables. The Banach fixed point theorem and a certain integral inequality with explicit estimate are used to establish the results.

On the boundedness of solutions for system of two-dimensional Volterra integral equations

Hącia L., Kaczmarek L.

Fasciculi Mathematici

1998

Nr 28

43-55

The sufficient conditions are given for the boundedness of solutions for a system oftwo-dimensionallinear Volterra integral equations.