Journal of Elliptic and Parabolic Equations

, Volume 4, Issue 1, pp 207–222 | Cite as

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

  • Renato Colucci


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.


Forward-backward diffusion Phase transitions Traveling waves 

Mathematics Subject Classification

Primary 35B36 35B10 35B25 35B40; Secondary 82C26 


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© Orthogonal Publishing and Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Dipartimento di IngegneriaUniversità degli Studi Niccolò CusanoRomeItaly

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