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Compact structures as true non-linear phenomena

1 Dipartimento di Scienze di Base e Applicate per l’Ingegneria, Sapienza Università di Roma, via A. Scarpa 16, I–00161, Roma, Italy
2 Dipartimento di Ingegneria, Università degli Studi di Perugia, Perugia, Italy
3 Institut de Recherche en Génie Civil et Mécanique, Ecole Centrale de Nantes, 1, rue de la Noë 44321 Nantes, France

$^\dagger$This contribution is part of the Special Issue: Nonlinear models in applied mathematics
  Guest Editor: Giuseppe Maria Coclite
  Link: http://www.aimspress.com/newsinfo/1213.html

Special Issues: Nonlinear models in applied mathematics

Traveling waves of permanent form with compact support are possible in several nonlinear partial nonlinear differential equations and this, mainly, along two pathways: A pure nonlinearity stronger than quadratic in the higher order gradient terms describing the mathematical model of the phenomena or a special inhomogeneity in quadratic gradient terms of the model. In the present note we perform a rigorous analysis of the mathematical structure of compactification via a generalization of a classical theorem by Weierstrass. Our mathematical analysis allows to explain in a rigorous and complete way the presence of compact structures in nonlinear partial differential equations 1 + 1 dimensions.
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Keywords phase coexistence; interface; compact waves; Weierstrass construction; travelling waves

Citation: Emilio N. M. Cirillo, Giuseppe Saccomandi, Giulio Sciarra. Compact structures as true non-linear phenomena. Mathematics in Engineering, 2019, 1(3): 434-446. doi: 10.3934/mine.2019.3.434

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