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Solitary waves for an equation related to a problem of microstructure formation

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Abstract

We prove the non existence of solitary wave solutions for an evolution equation related to a problem of microstructure formation. Moreover, we analyze in detail the ODEs system describing traveling waves and characterize bounded and unbounded solutions. Finally we construct an oscillating approximate solution and provide numerical simulations in order to illustrate the theoretical results.

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  1. Dipartimento di Ingegneria, Università degli Studi Niccolò Cusano, via Don Carlo Gnocchi, 3, 00166, Rome, Italy

    Renato Colucci

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  1. Renato Colucci
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Correspondence to Renato Colucci.

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Colucci, R. Solitary waves for an equation related to a problem of microstructure formation. J Elliptic Parabol Equ 4, 207–222 (2018). https://doi.org/10.1007/s41808-018-0016-3

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  • DOI: https://doi.org/10.1007/s41808-018-0016-3

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