For the equationwhere yK(y) > 0 for y = 0) in D, bounded by a Jordan (non-selfintersecting) "elliptic" arc Γ (for > 0) with endpoints A(0, 0)and B(l, 0), l > 0, and for y < 0 by a characteristic γ 1 through A which meets the characteristic γ 2 through B at the points C, the uniqueness of the Morawetz problem is proved without assuming that Γ is monotone.
The paper presents
findings on the kinetic regularities of polyisoprene
production in the presence of neodymium-based catalytic systems for
large-scale production processes. A mathematical model has been developed
for batch and continuous isoprene polymerization. The study identified
dependences of changes in the number-average and mass-average molecular
weight of the resulting product on the length of the applied reactor
cascade under continuous static operation. The description of the
continuous production mode leads to the necessity of analyzing the
structure of the flows by means of the distribution functions of the
residence time in the reactor, which is the basis for the formation
of a block of modules of the hydrodynamic level. A change in the length
of the reactor cascade leads to a change in the residence time of
particles in the reactor and, consequently, to a change in the hydrodynamic
regime. With the help of mathematical modeling tools, the influence
of the hydrodynamic regime in the reaction zone on the molecular weight
distribution of the resulting product is revealed.
The article considers the problem of damping vibrations of the beam for a nonlinear equation in the case of rigidly fixed ends. It is proved that solution to a nonlinear beam equation is uniquely. It is shown that under certain conditions on the coefficients of the solution of the problem will be oscillating.
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