Transformation of linear constant system equations

1967 ◽  
Vol 114 (4) ◽  
pp. 541 ◽  
Author(s):  
H.H. Rosenbrock
Keyword(s):  
System Equations ◽  
Linear Constant System ◽  
Constant System

A New Evaluation of the Mean Square Integral

1971 ◽  
Vol 93 (4) ◽  
pp. 242-246 ◽  
Author(s):  
R. J. Beshara
Keyword(s):  
Mean Square ◽  
Random Input ◽  
Order Linear ◽  
The Mean ◽  
Linear Constant System ◽  
Constant System

This paper gives a new evaluation of the mean square integral for an nth order, linear constant system forced by a random input. The results are explicit and literal. A comparison of Mersman’s determinant form and the results of this article show the overall superiority of this method.

scholarly journals An asymptotic analysis for a generalized Cahn–Hilliard system with fractional operators

2021 ◽  
Author(s):  
Pierluigi Colli ◽  
Gianni Gilardi ◽  
Jürgen Sprekels
Keyword(s):  
Additional Term ◽  
Linear Operators ◽  
Phase Variable ◽  
Logarithmic Potentials ◽  
Relaxation Problem ◽  
System Equations ◽  
Indicator Functions ◽  
Regularity Results ◽  
Compact Resolvents ◽  
Densely Defined

AbstractIn the recent paper “Well-posedness and regularity for a generalized fractional Cahn–Hilliard system” (Colli et al. in Atti Accad Naz Lincei Rend Lincei Mat Appl 30:437–478, 2019), the same authors have studied viscous and nonviscous Cahn–Hilliard systems of two operator equations in which nonlinearities of double-well type, like regular or logarithmic potentials, as well as nonsmooth potentials with indicator functions, were admitted. The operators appearing in the system equations are fractional powers $$A^{2r}$$ A 2 r and $$B^{2\sigma }$$ B 2 σ (in the spectral sense) of general linear operators A and B, which are densely defined, unbounded, selfadjoint, and monotone in the Hilbert space $$L^2(\Omega )$$ L 2 ( Ω ) , for some bounded and smooth domain $$\Omega \subset {{\mathbb {R}}}^3$$ Ω ⊂ R 3 , and have compact resolvents. Existence, uniqueness, and regularity results have been proved in the quoted paper. Here, in the case of the viscous system, we analyze the asymptotic behavior of the solution as the parameter $$\sigma $$ σ appearing in the operator $$B^{2\sigma }$$ B 2 σ decreasingly tends to zero. We prove convergence to a phase relaxation problem at the limit, and we also investigate this limiting problem, in which an additional term containing the projection of the phase variable on the kernel of B appears.

Characterization of chaotic vibration without system equations

1997 ◽  
Vol 32 (3) ◽  
pp. 547-562 ◽  
Author(s):  
Katsutoshi Yoshida ◽  
Keijin Sato ◽  
Sumio Yamamoto ◽  
Kazutaka Yokota
Keyword(s):  
Chaotic Vibration ◽  
System Equations
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