Abstract
In this paper, we study a fourth order semilinear parabolic equation on the infinite real line. We show that in a certain parameter range, this equation has propagating front solutions (solutions tending to 0 at +∞ and advancing to the right with a speedc) which leave behind them aperiodic pattern in the laboratory frame. This is thus an example of spontaneous pattern formation.
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Communicated by A. Jaffe
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Collet, P., Eckmann, J.P. The existence of dendritic fronts. Commun.Math. Phys. 107, 39–92 (1986). https://doi.org/10.1007/BF01206953
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DOI: https://doi.org/10.1007/BF01206953