Note on quantitative homogenization results for parabolic systems in Rd

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Note on quantitative homogenization results for parabolic systems in R^d. / Meshkova, Yulia.

In: Journal of Evolution Equations, Vol. 21, No. 1, 03.2021, p. 763 - 769.

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

Author

Meshkova, Yulia. / Note on quantitative homogenization results for parabolic systems in R^d. In: Journal of Evolution Equations. 2021 ; Vol. 21, No. 1. pp. 763 - 769.

BibTeX

@article{b87b9b62f6f84ecbbf563ff7233ef904,

title = "Note on quantitative homogenization results for parabolic systems in Rd",

abstract = "In L2(Rd; Cn) , we consider a semigroup e-tAε, t⩾ 0 , generated by a matrix elliptic second-order differential operator Aε⩾ 0. Coefficients of Aε are periodic, depend on x/ ε, and oscillate rapidly as ε→ 0. Approximations for e-tAε were obtained by Suslina (Funktsional Analiz i ego Prilozhen 38(4):86–90, 2004) and Suslina (Math Model Nat Phenom 5(4):390–447, 2010) via the spectral method and by Zhikov and Pastukhova (Russ J Math Phys 13(2):224–237, 2006) via the shift method. In the present note, we give another short proof based on the contour integral representation for the semigroup and approximations for the resolvent with two-parametric error estimates obtained by Suslina (2015).",

keywords = "Convergence rates, Homogenization, Parabolic systems, Trotter–Kato theorem, Trotter-Kato theorem",

author = "Yulia Meshkova",

year = "2021",

month = mar,

doi = "10.1007/s00028-020-00600-2",

language = "English",

volume = "21",

pages = "763 -- 769",

journal = "Journal of Evolution Equations",

issn = "1424-3199",

publisher = "Birkh{\"a}user Verlag AG",

number = "1",

}

RIS

TY - JOUR

T1 - Note on quantitative homogenization results for parabolic systems in Rd

AU - Meshkova, Yulia

PY - 2021/3

Y1 - 2021/3

N2 - In L2(Rd; Cn) , we consider a semigroup e-tAε, t⩾ 0 , generated by a matrix elliptic second-order differential operator Aε⩾ 0. Coefficients of Aε are periodic, depend on x/ ε, and oscillate rapidly as ε→ 0. Approximations for e-tAε were obtained by Suslina (Funktsional Analiz i ego Prilozhen 38(4):86–90, 2004) and Suslina (Math Model Nat Phenom 5(4):390–447, 2010) via the spectral method and by Zhikov and Pastukhova (Russ J Math Phys 13(2):224–237, 2006) via the shift method. In the present note, we give another short proof based on the contour integral representation for the semigroup and approximations for the resolvent with two-parametric error estimates obtained by Suslina (2015).

AB - In L2(Rd; Cn) , we consider a semigroup e-tAε, t⩾ 0 , generated by a matrix elliptic second-order differential operator Aε⩾ 0. Coefficients of Aε are periodic, depend on x/ ε, and oscillate rapidly as ε→ 0. Approximations for e-tAε were obtained by Suslina (Funktsional Analiz i ego Prilozhen 38(4):86–90, 2004) and Suslina (Math Model Nat Phenom 5(4):390–447, 2010) via the spectral method and by Zhikov and Pastukhova (Russ J Math Phys 13(2):224–237, 2006) via the shift method. In the present note, we give another short proof based on the contour integral representation for the semigroup and approximations for the resolvent with two-parametric error estimates obtained by Suslina (2015).

KW - Convergence rates

KW - Homogenization

KW - Parabolic systems

KW - Trotter–Kato theorem

KW - Trotter-Kato theorem

UR - http://www.scopus.com/inward/record.url?scp=85087735095&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/238a285f-6f96-3819-b291-4e9113deaad2/

U2 - 10.1007/s00028-020-00600-2

DO - 10.1007/s00028-020-00600-2

M3 - Article

AN - SCOPUS:85087735095

VL - 21

SP - 763

EP - 769

JO - Journal of Evolution Equations

JF - Journal of Evolution Equations

SN - 1424-3199

IS - 1

ER -

ID: 62079340