CPAA
Stability of Suliciu model for phase transitions
Shaoqiang Tang Huijiang Zhao
Communications on Pure & Applied Analysis 2004, 3(4): 545-556 doi: 10.3934/cpaa.2004.3.545
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.
keywords: Phase transition Laplace transform stability
DCDS-B
Positive entropic schemes for a nonlinear fourth-order parabolic equation
José A. Carrillo Ansgar Jüngel Shaoqiang Tang
Discrete & Continuous Dynamical Systems - B 2003, 3(1): 1-20 doi: 10.3934/dcdsb.2003.3.1
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.
keywords: long-time behavior of discrete solutions. Finite difference method discrete entropy estimates discrete positive solutions

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