TY - JOUR

T1 - High-frequency homogenization of multidimensional hyperbolic equations

AU - Дородный, Марк Александрович

PY - 2024/6/2

Y1 - 2024/6/2

N2 - In (Formula presented.), we consider an elliptic differential operator (Formula presented.), (Formula presented.), of the form (Formula presented.) with periodic coefficients. For hyperbolic equations with the operator (Formula presented.), analogs of homogenization problems related to an arbitrary point of the dispersion relation of the operator (Formula presented.) are studied (the so-called high-frequency homogenization). For the solutions of the Cauchy problems for these equations with special initial data, approximations in (Formula presented.) -norm for small ε are obtained.

AB - In (Formula presented.), we consider an elliptic differential operator (Formula presented.), (Formula presented.), of the form (Formula presented.) with periodic coefficients. For hyperbolic equations with the operator (Formula presented.), analogs of homogenization problems related to an arbitrary point of the dispersion relation of the operator (Formula presented.) are studied (the so-called high-frequency homogenization). For the solutions of the Cauchy problems for these equations with special initial data, approximations in (Formula presented.) -norm for small ε are obtained.

KW - 35B27

KW - Periodic differential operators

KW - effective operator

KW - homogenization

KW - hyperbolic equations

KW - operator error estimates

KW - spectral bands

UR - https://www.mendeley.com/catalogue/2a756403-33f5-3969-b3db-637b40e02e7c/

U2 - 10.1080/00036811.2024.2358136

DO - 10.1080/00036811.2024.2358136

M3 - Article

JO - Applicable Analysis

JF - Applicable Analysis

SN - 0003-6811

ER -