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Some personal remarks about applications of mathematics

Tadeusz Nadzieja — 2014

Mathematica Applicanda

Need to develop applications of mathematics meets with acceptance, understanding and sympathetic interest in the mathematicians world. Evidenced are by creation of the mathematics major with ... or the mathematics in ..., adding in a purely mathematical work of a few sentences or even a chapter on the possible applications of the results, conference papers often are preceded by an introductory discussion the motivations of the biological, physical or chemical character to deal with the issue. Organized...

A class of nonlocal parabolic problems occurring in statistical mechanics

Piotr BilerTadeusz Nadzieja — 1993

Colloquium Mathematicae

We consider parabolic equations with nonlocal coefficients obtained from the Vlasov-Fokker-Planck equations with potentials. This class of equations includes the classical Debye system from electrochemistry as well as an evolution model of self-attracting clusters under friction and fluctuations. The local in time existence of solutions to these equations (with no-flux boundary conditions) and properties of stationary solutions are studied.

Stationary solutions of aerotaxis equations

Piotr KnosallaTadeusz Nadzieja — 2015

Applicationes Mathematicae

We study the existence and uniqueness of the steady state in a model describing the evolution of density of bacteria and oxygen dissolved in water filling a capillary. The steady state is a stationary solution of a nonlinear and nonlocal problem which depends on the energy function and contains two parameters: the total mass of the colony of bacteria and the concentration (or flux) of oxygen at the end of the capillary. The existence and uniqueness of solutions depend on relations between these...

Evolution in a migrating population model

Włodzimierz BąkTadeusz Nadzieja — 2012

Applicationes Mathematicae

We consider a model of migrating population occupying a compact domain Ω in the plane. We assume the Malthusian growth of the population at each point x ∈ Ω and that the mobility of individuals depends on x ∈ Ω. The evolution of the probability density u(x,t) that a randomly chosen individual occupies x ∈ Ω at time t is described by the nonlocal linear equation u t = Ω φ ( y ) u ( y , t ) d y - φ ( x ) u ( x , t ) , where φ(x) is a given function characterizing the mobility of individuals living at x. We show that the asymptotic behaviour of u(x,t)...

Existence and nonexistence of solutions for a model of gravitational interaction of particles, II

Piotr BilerDanielle HilhorstTadeusz Nadzieja — 1994

Colloquium Mathematicae

We study the existence and nonexistence in the large of radial solutions to a parabolic-elliptic system with natural (no-flux) boundary conditions describing the gravitational interaction of particles. The blow-up of solutions defined in the n-dimensional ball with large initial data is connected with the nonexistence of radial stationary solutions with a large mass.

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