Sobolev type inequalities of time-periodic boundary value problems for Heaviside and Thomson cables

Boundary value problems

Kohtaro Watanabe¹  Yoshinori Kametaka²  Atsushi Nagai³  Kazuo Takemura³  Hiroyuki Yamagishi⁴ 

[1] Department of Computer Science, National Defense Academy, Yokosuka, Japan;Faculty of Engineering Science, Osaka University, Toyonaka, Japan;Liberal Arts and Basic Sciences, College of Industrial Technology, Nihon University, Narashino, Japan;Tokyo Metropolitan College of Industrial Technology, Shinagawa, Tokyo, Japan

关键词: Hurwitz polynomial;    Sobolev inequality;    best constant;    Green function;    n-cascaded LRCG circuits;   

DOI  :  10.1186/1687-2770-2012-95

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

We consider a time-periodic boundary value problem of n th order ordinary differential operator which appears typically in Heaviside cable and Thomson cable theory. We calculate the best constant and a family of the best functions for a Sobolev type inequality by using the Green function and apply its results to the cable theory. Physical meaning of a Sobolev type inequality is that we can estimate the square of maximum of the absolute value of AC output voltage from above by the power of input voltage. MSC:46E35, 41A44, 34B27.

【 授权许可】

CC BY