Analytical and numerical investigation of traveling waves for the Allen–Cahn model with relaxation
2016 ◽
Vol 26
(05)
◽
pp. 931-985
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Keyword(s):
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.
2014 ◽
Vol 24
(06)
◽
pp. 1165-1195
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2021 ◽
2012 ◽
pp. 519-526
Keyword(s):
2018 ◽
Vol 265
(6)
◽
pp. 2577-2613
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On the Existence and Stability of Fast Traveling Waves in a Doubly Diffusive FitzHugh--Nagumo System
2018 ◽
Vol 17
(1)
◽
pp. 754-787
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2019 ◽
Vol 12
(01)
◽
pp. 1950004
2020 ◽
Vol 268
(7)
◽
pp. 3449-3496
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Keyword(s):
2013 ◽
Vol 397
(1)
◽
pp. 322-333
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