From polynomial integrals of Hamiltonian flows to a model of non-linear elasticity

Misha Bialy; Andrey E. Mironov

doi:10.1016/j.jde.2013.07.040

From polynomial integrals of Hamiltonian flows to a model of non-linear elasticity

Misha Bialy
, Andrey E. Mironov

School of Mathematical Sciences

Tel Aviv University

Research output: Contribution to journal › Article › peer-review

Abstract

We prove non-existence of smooth solutions of a quasi-linear system suggested by Ericksen in a model of Non-linear Elasticity. This system is of mixed elliptic-hyperbolic type. We discuss also a relation of such a system to polynomial integrals of Classical Hamiltonian systems.

Original language	English GB
Pages (from-to)	3434-3446
Number of pages	13
Journal	Journal of Differential Equations
Volume	255
Issue number	10
DOIs	https://doi.org/10.1016/j.jde.2013.07.040
State	Published - 15 Nov 2013

Keywords

Blow-up
Genuine non-linearity
P-system
Polynomial integrals

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jde.2013.07.040

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@article{78ddc1c7f5b14767b68832c81041cd36,

title = "From polynomial integrals of Hamiltonian flows to a model of non-linear elasticity",

abstract = "We prove non-existence of smooth solutions of a quasi-linear system suggested by Ericksen in a model of Non-linear Elasticity. This system is of mixed elliptic-hyperbolic type. We discuss also a relation of such a system to polynomial integrals of Classical Hamiltonian systems.",

keywords = "Blow-up, Genuine non-linearity, P-system, Polynomial integrals",

author = "Misha Bialy and Mironov, \{Andrey E.\}",

note = "Funding Information: M.B. was supported in part by ISF grant 128/10 and A.M. was supported by the Presidium of the Russian Academy of Sciences (under the program “Nonlinear Systems in Geometry”); grant MD-5134.2012.1 from the President of Russia ; and a grant from Dmitri Ziminʼs “Dynasty” foundation . It is our pleasure to thank these funds for the support.",

year = "2013",

month = nov,

day = "15",

doi = "10.1016/j.jde.2013.07.040",

language = "الإنجليزيّة",

volume = "255",

pages = "3434--3446",

journal = "Journal of Differential Equations",

issn = "0022-0396",

publisher = "Academic Press Inc.",

number = "10",

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TY - JOUR

T1 - From polynomial integrals of Hamiltonian flows to a model of non-linear elasticity

AU - Bialy, Misha

AU - Mironov, Andrey E.

N1 - Funding Information: M.B. was supported in part by ISF grant 128/10 and A.M. was supported by the Presidium of the Russian Academy of Sciences (under the program “Nonlinear Systems in Geometry”); grant MD-5134.2012.1 from the President of Russia ; and a grant from Dmitri Ziminʼs “Dynasty” foundation . It is our pleasure to thank these funds for the support.

PY - 2013/11/15

Y1 - 2013/11/15

N2 - We prove non-existence of smooth solutions of a quasi-linear system suggested by Ericksen in a model of Non-linear Elasticity. This system is of mixed elliptic-hyperbolic type. We discuss also a relation of such a system to polynomial integrals of Classical Hamiltonian systems.

AB - We prove non-existence of smooth solutions of a quasi-linear system suggested by Ericksen in a model of Non-linear Elasticity. This system is of mixed elliptic-hyperbolic type. We discuss also a relation of such a system to polynomial integrals of Classical Hamiltonian systems.

KW - Blow-up

KW - Genuine non-linearity

KW - P-system

KW - Polynomial integrals

UR - https://www.scopus.com/pages/publications/84883049597

U2 - 10.1016/j.jde.2013.07.040

DO - 10.1016/j.jde.2013.07.040

M3 - مقالة

SN - 0022-0396

VL - 255

SP - 3434

EP - 3446

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 10

ER -

From polynomial integrals of Hamiltonian flows to a model of non-linear elasticity

Abstract

Keywords

ASJC Scopus subject areas

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