Mathematical Methods in the Applied Sciences

Volume 42, Issue 3 pp. 871-882

RESEARCH ARTICLE

Upper semicontinuity of global attractors for a viscoelastic equations with nonlinear density and memory effects

Yony Raúl Santaria Leuyacc,

Corresponding Author

Yony Raúl Santaria Leuyacc

[email protected]

orcid.org/0000-0001-8279-7460

Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, São Carlos-SP, Brazil

Facultad de Ciencias Matemáticas, Universidad Nacional Mayor de San Marcos, Lima, Perú

Correspondence

Yony Raúl Santaria Leuyacc, Matemáticas e de Computação, Universidade de São Paulo, São Carlos-SP 13560-970, Brazil.

Email: [email protected]

Communicated by: K. Yildirim

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Jorge Luis Crisostomo Parejas,

Jorge Luis Crisostomo Parejas

orcid.org/0000-0002-9049-4125

Dirección de estudios generales, Universidad San Ignacio de Loyola, Lima, Peru

Facultad de Ciencias Matemáticas, Universidad Nacional Mayor de San Marcos, Lima, Perú

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Yony Raúl Santaria Leuyacc,

Corresponding Author

Yony Raúl Santaria Leuyacc

[email protected]

orcid.org/0000-0001-8279-7460

Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, São Carlos-SP, Brazil

Facultad de Ciencias Matemáticas, Universidad Nacional Mayor de San Marcos, Lima, Perú

Correspondence

Yony Raúl Santaria Leuyacc, Matemáticas e de Computação, Universidade de São Paulo, São Carlos-SP 13560-970, Brazil.

Email: [email protected]

Communicated by: K. Yildirim

Search for more papers by this author

Jorge Luis Crisostomo Parejas,

Jorge Luis Crisostomo Parejas

orcid.org/0000-0002-9049-4125

Dirección de estudios generales, Universidad San Ignacio de Loyola, Lima, Peru

Facultad de Ciencias Matemáticas, Universidad Nacional Mayor de San Marcos, Lima, Perú

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First published: 04 December 2018

https://doi.org/10.1002/mma.5389

Citations: 4

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Abstract

This paper is devoted to showing the upper semicontinuity of global attractors associated with the family of nonlinear viscoelastic equations

$urn:x-wiley:mma:media:mma5389:mma5389-math-0001$

in a three-dimensional space, for f growing up to the critical exponent and dependent on ρ ∈ [0,4), as ρ→0⁺. This equation models extensional vibrations of thin rods with nonlinear material density ϱ(∂_tu) = |∂_tu|^ρ and presence of memory effects. This type of problems has been extensively studied by several authors; the existence of a global attractor with optimal regularity for each ρ ∈ [0,4) were established only recently. The proof involves the optimal regularity of the attractors combined with Hausdorff's measure.

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Volume42, Issue3

February 2019

Pages 871-882

Upper semicontinuity of global attractors for a viscoelastic equations with nonlinear density and memory effects

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Upper semicontinuity of global attractors for a viscoelastic equations with nonlinear density and memory effects

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