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  Quarterly of Applied Mathematics
Quarterly of Applied Mathematics
  
Online ISSN 1552-4485; Print ISSN 0033-569X
 

A nonlinear model describing a short wave-long wave interaction in a viscoelastic medium


Authors: Paulo Amorim and João Paulo Dias
Journal: Quart. Appl. Math. 71 (2013), 417-432
MSC (2010): Primary 35M31
Published electronically: October 1, 2012
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Abstract: In this paper we introduce a system coupling a nonlinear Schrödinger equation with a system of viscoelasticity, modeling the interaction between short and long waves, acting for instance on media such as plasmas or polymers. We prove the existence and uniqueness of local (in time) strong solutions and the existence of global weak solutions for the corresponding Cauchy problem. In particular we extend previous results in [Nohel et. al., Commun. Part. Diff. Eq., 13 (1988)] for the quasilinear system of viscoelasticity. We finish with some numerical computations to illustrate our results.


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Additional Information

Paulo Amorim
Affiliation: Centro de Matemática e Aplicações Fundamentais, FCUL, Av. Prof. Gama Pinto 2, 1649-003 Lisboa, Portugal
Email: pamorim@ptmat.fc.ul.pt

João Paulo Dias
Affiliation: Centro de Matemática e Aplicações Fundamentais, FCUL, Av. Prof. Gama Pinto 2, 1649-003 Lisboa, Portugal
Email: dias@ptmat.fc.ul.pt

DOI: http://dx.doi.org/10.1090/S0033-569X-2012-01298-4
PII: S 0033-569X(2012)01298-4
Received by editor(s): May 30, 2011
Published electronically: October 1, 2012
Additional Notes: The authors were supported by FCT, through Financiamento Base 2008-ISFL-1-209 and the FCT grant PTDC/MAT/110613/2009. The first author was also supported by FCT through a Ciência 2008 fellowship
Article copyright: © Copyright 2012 Brown University
The copyright for this article reverts to public domain 28 years after publication.



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