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In this paper we propose a mathematical model to describe the evolution of leukemia
in the bone marrow. The model is based on a reaction-diffusion system of equations in a porous
medium. We show the existence of two stationary solutions, one of them corresponds to the normal
case and another one to the pathological case. The leukemic state appears as a result of a bifurcation
when the normal state loses its stability. The critical conditions of leukemia development
are determined by the proliferation...
In this paper we present an analysis of the partial differential equations that
describe the Chemical Vapor Infiltration (CVI) processes. The mathematical model
requires at least two partial differential equations, one describing the
gas phase and one corresponding to the solid phase.
A key difficulty in the process is the long processing times that are typically
required. We address here the issue of optimization and show that we can choose
appropriate pressure and temperature to minimize these...
We investigate different asymptotic regimes for Vlasov equations modeling the evolution of a cloud of particles in a turbulent flow. In one case we obtain a convection or a convection-diffusion effective equation on the concentration of particles. In the second case, the effective model relies on a Vlasov-Fokker-Planck equation.
We investigate different asymptotic regimes
for Vlasov equations modeling the evolution of a cloud of particles in a turbulent flow. In one case we obtain a convection or a convection-diffusion effective equation on the concentration of particles. In the second case, the effective model relies on a Vlasov-Fokker-Planck equation.
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