当前位置: X-MOL 学术Funct. Anal. Its Appl. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Operator Error Estimates for Homogenization of Hyperbolic Equations
Functional Analysis and Its Applications ( IF 0.6 ) Pub Date : 2020-09-02 , DOI: 10.1134/s0016266320010074
M. A. Dorodnyi , T. A. Suslina

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 1/2ε τ) and A 1/2ε sin(A 1/2ε τ) 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 1/2ε τ) in the (HsH1)-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 2τ uε = − uε.

中文翻译:

双曲方程均化的算子误差估计

甲自伴随强烈椭圆二阶微分算子ε大号2(ℝ d ;ℂ Ñ)被认为。假定的系数ε是周期性的,并且依赖于X / ε,其中ε > 0是一个小的参数。近似为运营商COS(1/2 ε τ)和1/2 ε SIN(1/2 ε τ从索伯列夫空间算的范数)ħ小号(ℝ d ;ℂ Ñ )到大号2(ℝ d ;ℂ Ñ)(对于适当的小号)获得。逼近为操作一个校正1/2 ε SIN(1/2 ε τ在)(ħ小号ħ 1)范数也被获得。研究了关于规范类型和估计依赖关系的结果的清晰度的问题。结果应用于研究Cauchy问题为双曲线方程解的行为2 τ Ù ε = - ù ε
更新日期:2020-09-02
down
wechat
bug