Oscillations in Compressible Navier-Stokes and Homogenization in Phase Transition problems
arxiv(2024)
摘要
In the first part of this article we present some exact solutions for special
hyperbolic-parabolic systems with sustained oscillations induced by the initial
data, most notably the compressible Navier-Stokes system with non-monotone
pressure. This part complements where such examples are
extensively studied. The second part deals with the problem of homogenization
for one-dimensional models describing phase transitions for viscoelastic
materials . Ideas from the kinetic formulation of conservation laws are
employed to derive effective equations that describe the propagation of
oscillations.
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