Abstract
The existence, uniqueness, stability and regularity properties of traveling-wave solutions of a bistable nonlinear integrodifferential equation are established, as well as their global asymptotic stability in the case of zero-velocity continuous waves. This equation is a direct analog of the more familiar bistable nonlinear diffusion equation, and shares many of its properties. It governs gradient flows for free-energy functionals with general nonlocal interaction integrals penalizing spatial nonuniformity.
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(Accepted October 16, 1995)
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Bates, P., Fife, P., Ren, X. et al. Traveling Waves in a Convolution Model for Phase Transitions. Arch Rational Mech Anal 138, 105–136 (1997). https://doi.org/10.1007/s002050050037
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DOI: https://doi.org/10.1007/s002050050037