High-frequency homogenization of multidimensional hyperbolic equations
Mark Aleksandrovich Dorodnyi · Applicable Analysis · 2024
In L2(Rd), we consider an elliptic differential operator Aϵ, ϵ>0, of the form Aϵ=−divg(x/ϵ)∇+ϵ−2V(x/ϵ) with periodic coefficients. For hyperbolic equations with the operator Aϵ, analogs of homogenization problems related to an arbitrary point of the dispersion relation of the operator A1 are studied (the so-called high-frequency homogenization). For the solutions of the Cauchy problems for these equations with special initial data, approximations in L2(Rd)-norm for small ε are obtained.