Sustained Oscillations in Hyperbolic-Parabolic Systems
Archive for Rational Mechanics and Analysis(2024)
摘要
We construct examples of oscillating solutions with persistent oscillations
for various hyperbolic-parabolic systems with singular diffusion matrices that
appear in mechanics. These include, an example for the equations of nonlinear
viscoelasticity of Kelvin-Voigt type with stored energy that violates rank-one
convexity, which amounts to a time-dependent variant of twinning solutions. An
example pertaining to the system of gas dynamics with thermal effects for a
viscous, adiabatic gas. Finally, an example for the compressible Navier-Stokes
system in one-space dimension with nonmonotone pressure function. We also study
the existence of oscillating solutions for linear hyperbolic-parabolic systems
with singular diffusion matrices.
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