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CPAA
We study stability of subsonic phase boundary solutions in the
Suliciu model for phase transitions under tri-linear structural
relation. With the help of Laplace transform, the evolution of
perturbation is described by a linear dynamical system, and
explicit solution is obtained in terms of inverse Laplace
transform. Stability is established through energy estimates. The
relaxed system is also discussed.
DCDS-B
A finite-difference scheme with positivity-preserving and
entropy-decreasing properties for a nonlinear fourth-order
parabolic equation arising in quantum systems and interface
fluctuations is derived. Initial-boundary value problems, the
Cauchy problem and a rescaled equation are discussed. Based on
this scheme we elucidate properties of the long-time asymptotics
for this equation.
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