100 research outputs found
Generalized Entropy Method for the Renewal Equation with Measure Data
We study the long-time asymptotics for the so-called McKendrick-Von Foerster
or renewal equation, a simple model frequently considered in structured
population dynamics. In contrast to previous works, we can admit a bounded
measure as initial data. To this end, we apply techniques from the calculus of
variations that have not been employed previously in this context. We
demonstrate how the generalized relative entropy method can be refined in the
Radon measure framework
Analysis of a viscosity model for concentrated polymers
The paper is concerned with a class of mathematical models for polymeric
fluids, which involves the coupling of the Navier-Stokes equations for a
viscous, incompressible, constant-density fluid with a parabolic-hyperbolic
integro-differential equation describing the evolution of the polymer
distribution function in the solvent, and a parabolic integro-differential
equation for the evolution of the monomer density function in the solvent. The
viscosity coefficient appearing in the balance of linear momentum equation in
the Navier-Stokes system includes dependence on the shear-rate as well as on
the weight-averaged polymer chain length. The system of partial differential
equations under consideration captures the impact of polymerization and
depolymerization effects on the viscosity of the fluid. We prove the existence
of global-in-time, large-data weak solutions under fairly general hypotheses.Comment: 26 page
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