When two miscible fluids, such as glycerol (glycerin) and water, are brought in contact, they immediately diffuse in each other. However if the diffusion is sufficiently slow, large concentration gradients exist during some time. They can lead to the appearance of an “effective interfacial tension”. To study these phenomena we use the mathematical model consisting of the diffusion equation with convective terms and of the Navier-Stokes equations with the Korteweg stress. We prove the global existence...
We study the null controllability by one control force of some linear systems of parabolic type. We give sufficient conditions for the null controllability property to be true and, in an abstract setting, we prove that it is not always possible to control.
We study the null controllability by one control force of some linear systems of parabolic type.
We give sufficient conditions for the null controllability
property to be true and, in an abstract setting, we prove that it
is not always possible to control.
When two miscible fluids, such as glycerol (glycerin) and water,
are brought in contact, they immediately diffuse in each other.
However if the diffusion is sufficiently slow, large concentration gradients exist
during some time. They can lead to the appearance of an
“effective interfacial tension”. To study these phenomena we
use the mathematical model
consisting of the diffusion equation with convective terms and of
the Navier-Stokes equations with the Korteweg stress.
We prove the global...
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