On a Static Compensation in the Galerkin Approximation Method for a Parabolic Distributed System

This study deals with the dynamical evolutions exhibited by a simple mechanical model of building, comprising a parallelepiped standing on a horizontal plane. The main goal is the introduction of a pendulum in order to reduce oscillations. The theoretical part of the work consists of a Lagrange formulation and Galerkin approximation method, and dry friction has also been considered. From the analytical/numerical simulations, we derive some important conclusions, providing us with the tools suitable for the design of absorbers in practical cases.

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Instability of Vertical Throughflows in Bidisperse Porous Media

Physics ◽

10.3390/physics3040052 ◽

2021 ◽

Vol 3 (4) ◽

pp. 821-828

Author(s):

Florinda Capone ◽

Roberta De Luca

Keyword(s):

Porous Media ◽

Rayleigh Number ◽

Closed Form ◽

Nonlinear Stability ◽

Approximation Method ◽

Galerkin Approximation ◽

Fluid Motion ◽

Linear Instability ◽

Stability Threshold ◽

Darcy Rayleigh Number

In this paper, the instability of a vertical fluid motion, or throughflow, is investigated in a horizontal bidisperse porous layer that is uniformly heated from below. By means of the order-1 Galerkin approximation method, the critical Darcy–Rayleigh number for the onset of steady instability is determined in closed form. The coincidence between the linear instability threshold and the global nonlinear stability threshold, in the energy norm, is shown.

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ASYMPTOTIC BEHAVIOR OF STOCHASTIC DISSIPATIVE QUANTUM ZAKHAROV EQUATIONS

Stochastics and Dynamics ◽

10.1142/s0219493712500165 ◽

2013 ◽

Vol 13 (02) ◽

pp. 1250016 ◽

Cited By ~ 3

Author(s):

YANFENG GUO ◽

BOLING GUO ◽

DONGLONG LI

Keyword(s):

Asymptotic Behavior ◽

White Noise ◽

Approximation Method ◽

Existence And Uniqueness ◽

A Priori Estimates ◽

A Priori ◽

Galerkin Approximation ◽

Uniqueness Of Solutions ◽

Asymptotic Behaviors ◽

Priori Estimates

The stochastic dissipative quantum Zakharov equations with white noise are studied. The existence and uniqueness of solutions are obtained by using the standard Galerkin approximation method on the basis of the time uniform a priori estimates in various spaces. Moreover, the asymptotic behaviors of the solutions for the stochastic dissipative quantum Zakharov equations with white noise are also investigated.

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A modified Galerkin approximation method for volterra equations with smooth kernels

Applied Mathematics and Computation ◽

10.1016/0096-3003(78)90027-9 ◽

1978 ◽

Vol 4 (1) ◽

pp. 67-79 ◽

Cited By ~ 3

Author(s):

John M. Bownds

Keyword(s):

Approximation Method ◽

Galerkin Approximation ◽

Volterra Equations ◽

Smooth Kernels

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A Study on Static Compensation in the Galerkin Approximation Method for a class of Distributed Systems

IEEJ Transactions on Electronics Information and Systems ◽

10.1541/ieejeiss1987.115.7_882 ◽

1995 ◽

Vol 115 (7) ◽

pp. 882-886

Author(s):

Jun IMAI ◽

Kiyoshi WADA ◽

Setsuo SAGARA

Keyword(s):

Distributed Systems ◽

Approximation Method ◽

Galerkin Approximation

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Global Existence for Stochastic Strongly Dissipative Zakharov Equations

Advances in Mathematical Physics ◽

10.1155/2020/2359780 ◽

2020 ◽

Vol 2020 ◽

pp. 1-19

Author(s):

Xueqin Wang ◽

Yadong Shang ◽

Chunlin Lei

Keyword(s):

Global Existence ◽

White Noise ◽

Approximation Method ◽

Stochastic Partial Differential Equations ◽

Existence And Uniqueness ◽

A Priori Estimates ◽

A Priori ◽

Galerkin Approximation ◽

Uniqueness Of Solutions ◽

Priori Estimates

The stochastic strongly dissipative Zakharov equations with white noise are studied. On the basis of the time uniform a priori estimates, we prove the existence and uniqueness of solutions in energy spaces E1 and E2, by using the standard Galerkin approximation method of stochastic partial differential equations.

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