Asymptotically homogeneous solutions of differential equations whose symbols are polynomials quasi-homogeneous with respect to one-parameter groups with generators containing a nilpotent component

Drozhzhinov Yu.N.; ZavYalov B.I.

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Asymptotically homogeneous solutions of differential equations whose symbols are polynomials quasi-homogeneous with respect to one-parameter groups with generators containing a nilpotent component

机译：相对于一参量群的符号为拟齐次多项式的微分方程的渐近齐次解，其中生成器包含幂等分量

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According to Theorem 2, the Laplace equation has a fundamental solution asymptotically homogeneous with respect to ρ_1(k) = k~2ρ (k) = lnk, and the wave equation has a fundamental solution asymptotically homogeneous with respect to ρ1(k) = k~2ρ(k) = 1. Thus, Theorem 2 clarifies the dependence of the asymptotics of a fundamental solution on the structure of the symbol of the equation.

机译：根据定理2，拉普拉斯方程具有相对于ρ_1（k）= k〜2ρ（k）= lnk渐近齐次的基本解，并且波动方程具有相对于ρ1（k）= k渐近齐次的基本解〜2ρ（k）=1。因此，定理2阐明了基本解的渐近性对方程符号结构的依赖性。

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《Doklady. Mathematics》 |2013年第2期|共3页
作者
Drozhzhinov Yu.N.; ZavYalov B.I.;
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正文语种 eng
中图分类数学;
关键词
Asymptotically; differential; component;

机译：渐近;微分;分量;

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专利

1. Asymptotically homogeneous solutions of differential equations whose symbols are polynomials quasi-homogeneous with respect to one-parameter groups with generators containing a nilpotent component [J] . Drozhzhinov Yu.N., ZavYalov B.I. Doklady. Mathematics . 2013,第2期

机译：相对于一参量群的符号为拟齐次多项式的微分方程的渐近齐次解，其中生成器包含幂等分量
2. Asymptotically Homogeneous Generalized Functions at Zero and Convolution Equations with Kernels Quasi-Homogeneous Polynomial Symbols [J] . Yu. N. Drozhzhinov, B. I. Zav’yalov Doklady. Mathematics . 2009,第3期

机译：具有核准齐次多项式符号的零和卷积方程的渐近齐次广义函数
3. Polynomial solutions of quasi-homogeneous partial differential equations [J] . LUO Xuebo, ZHENG Zhujun Science in China. Series A . 2001,第9期

机译：拟齐次偏微分方程的多项式解
4. About the polynomial solutions of homogeneous linear differential equations depending on parameters [C] . Delphine Boucher International symposium on Symbolic and algebraic computation . 1999

机译：关于取决于参数的齐次线性微分方程的多项式解
5. On the Improved Asymptotics for Oscillatory Solutions of Second Order Ordinary Differential Equations. [D] . Heitman, Zhu Wang. 2014

机译：二阶常微分方程振动解的改进渐近性。
6. Asymptotic Bounds for the Time-Periodic Solutions to the Singularly Perturbed Ordinary Differential Equations [O] . Gabil M. Amiraliyev, Aysenur Ucar 2013

机译：奇摄动常微分方程时间周期解的渐近界
7. SOLUTION ALGEBRAS OF DIFFERENTIAL EQUATIONS AND QUASI-HOMOGENEOUS VARIETIES: A NEW DIFFERENTIAL GALOIS CORRESPONDENCE [O] . Yves Andr ´e 2016

机译：求解微分方程和准齐次变量的代数：一种新的微分GaLOIs对应
8. Expansions in Series of Homogeneous Polynomial Solutions of the General Two-Dimensional Linear Partial Differential Equation of the Second Order with Constant Coefficients [R] . D. V. Widder 1958

机译：常系数二阶一般二维线性偏微分方程齐次多项式解的一系列展开式

Asymptotically homogeneous solutions of differential equations whose symbols are polynomials quasi-homogeneous with respect to one-parameter groups with generators containing a nilpotent component

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