Analytical and numerical investigation of traveling waves for the Allen-Cahn model with relaxation

作者：Lattanzio Corrado; Mascia Corrado; Plaza Ramon G^*; Simeoni Chiara

来源：Mathematical Models and Methods in Applied Sciences, 2016, 26(5): 931-985.

DOI：10.1142/S0218202516500226

• Allen-Cahn equation
• traveling waves
• nonlinear stability

A modification of the parabolic Allen-Cahn equation, determined by the substitution of Fick's diffusion law with a relaxation relation of Cattaneo-Maxwell type, is considered. The analysis concentrates on traveling fronts connecting the two stable states of the model, investigating both the aspects of existence and stability. The main contribution is the proof of the nonlinear stability of the wave, as a consequence of detailed spectral and linearized analyses. In addition, numerical studies are performed in order to determine the propagation speed, to compare it to the speed for the parabolic case, and to explore the dynamics of large perturbations of the front.

• 出版日期2016-5