A kinetic model of tumor/immune system cellular interactions.
On bilinear kinetic equations. Between micro and macro descriptions of biological populations
In this paper a general class of Boltzmann-like bilinear integro-differential systems of equations (GKM, Generalized Kinetic Models) is considered. It is shown that their solutions can be approximated by the solutions of appropriate systems describing the dynamics of individuals undergoing stochastic interactions (at the "microscopic level"). The rate of approximation can be controlled. On the other hand the GKM result in various models known in biomathematics (at the "macroscopic level") including...
Mathematical models in biology - an introduction
The article contains no abstract
Review: Nonlinear Dynamical Systems and Chaos Edited by H. W. Broer, S. A. van Gils, I. Hoveijn and F. Takens
The article contains no abstract
Some remarks on applied mathematics – written by the applied mathematician
Terms ,,the application of mathematics '' and ,,applied mathematics'' are often used interchangeably. Some people, however, give them different meanings. I prefer the latter term, because it is the name of this field in most languages, the names of departments, names of well-known magazines, etc. While the term "the application of mathematics" suggests the use of previously developed methods, the term "applied mathematics" indicates a new quality that distinguishes it from theoretical mathematics,...
A nonlocal coagulation-fragmentation model
A new nonlocal discrete model of cluster coagulation and fragmentation is proposed. In the model the spatial structure of the processes is taken into account: the clusters may coalesce at a distance between their centers and may diffuse in the physical space Ω. The model is expressed in terms of an infinite system of integro-differential bilinear equations. We prove that some results known in the spatially homogeneous case can be extended to the nonlocal model. In contrast to the corresponding local...
Around the Kato generation theorem for semigroups
We show that the result of Kato on the existence of a semigroup solving the Kolmogorov system of equations in l₁ can be generalized to a larger class of the so-called Kantorovich-Banach spaces. We also present a number of related generation results that can be proved using positivity methods, as well as some examples.
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