Operator error estimates for homogenization of hyperbolic equations

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Operator error estimates for homogenization of hyperbolic equations. / Suslina, T. A. ; Dorodnyi, M. .

In: Functional Analysis and its Applications, Vol. 54, No. 1, 01.01.2020, p. 53-58.

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

BibTeX

@article{63cb25e0349e4f9999214763d5c35c9d,

title = "Operator error estimates for homogenization of hyperbolic equations",

abstract = "A self-adjoint strongly elliptic second-order differential operator Aε on L2(ℝd;ℂn) is considered. It is assumed that the coefficients of Aε are periodic and depend on x/ε, where ε > 0 is a small parameter. Approximations for the operators cos(A 1/2ετ) and A 1/2ε sin(A 1/2ετ) in the norm of operators from the Sobolev space Hs(ℝd;ℂn) to L2(ℝd;ℂn) (for appropriate s) are obtained. Approximation with a corrector for the operator A 1/2ε sin(A 1/2ετ) in the (Hs → H1)-norm is also obtained. The question about the sharpness of the results with respect to the norm type and with respect to the dependence of the estimates on is studied. The results are applied to study the behavior of the solutions of the Cauchy problem for the hyperbolic equation ∂ 2τuε = − Aεuε.",

keywords = "Periodic differential operators, homogenization, operator error estimates, hyperbolic equations, periodic differential operators",

author = "Suslina, {T. A.} and M. Dorodnyi",

note = "Publisher Copyright: {\textcopyright} 2020, Pleiades Publishing, Ltd.",

year = "2020",

month = jan,

day = "1",

doi = "10.1134/S0016266320010074",

language = "English",

volume = "54",

pages = "53--58",

journal = "Functional Analysis and its Applications",

issn = "0016-2663",

publisher = "Springer Nature",

number = "1",

}

RIS

TY - JOUR

T1 - Operator error estimates for homogenization of hyperbolic equations

AU - Suslina, T. A.

AU - Dorodnyi, M.

PY - 2020/1/1

Y1 - 2020/1/1

N2 - A self-adjoint strongly elliptic second-order differential operator Aε on L2(ℝd;ℂn) is considered. It is assumed that the coefficients of Aε are periodic and depend on x/ε, where ε > 0 is a small parameter. Approximations for the operators cos(A 1/2ετ) and A 1/2ε sin(A 1/2ετ) in the norm of operators from the Sobolev space Hs(ℝd;ℂn) to L2(ℝd;ℂn) (for appropriate s) are obtained. Approximation with a corrector for the operator A 1/2ε sin(A 1/2ετ) in the (Hs → H1)-norm is also obtained. The question about the sharpness of the results with respect to the norm type and with respect to the dependence of the estimates on is studied. The results are applied to study the behavior of the solutions of the Cauchy problem for the hyperbolic equation ∂ 2τuε = − Aεuε.

AB - A self-adjoint strongly elliptic second-order differential operator Aε on L2(ℝd;ℂn) is considered. It is assumed that the coefficients of Aε are periodic and depend on x/ε, where ε > 0 is a small parameter. Approximations for the operators cos(A 1/2ετ) and A 1/2ε sin(A 1/2ετ) in the norm of operators from the Sobolev space Hs(ℝd;ℂn) to L2(ℝd;ℂn) (for appropriate s) are obtained. Approximation with a corrector for the operator A 1/2ε sin(A 1/2ετ) in the (Hs → H1)-norm is also obtained. The question about the sharpness of the results with respect to the norm type and with respect to the dependence of the estimates on is studied. The results are applied to study the behavior of the solutions of the Cauchy problem for the hyperbolic equation ∂ 2τuε = − Aεuε.

KW - Periodic differential operators

KW - homogenization

KW - operator error estimates

KW - hyperbolic equations

KW - periodic differential operators

UR - https://link.springer.com/article/10.1134/S0016266320010074

UR - http://www.scopus.com/inward/record.url?scp=85090081633&partnerID=8YFLogxK

U2 - 10.1134/S0016266320010074

DO - 10.1134/S0016266320010074

M3 - Article

VL - 54

SP - 53

EP - 58

JO - Functional Analysis and its Applications

JF - Functional Analysis and its Applications

SN - 0016-2663

IS - 1

ER -

ID: 61240079