scholarly journals Degenerated and Competing Dirichlet Problems with Weights and Convection

Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 271
Author(s):  
Dumitru Motreanu
Keyword(s):  
Dirichlet Boundary ◽  
Differential Operators ◽  
Weighted Sobolev Spaces ◽  
Convection Term ◽  
Dirichlet Problems ◽  
Finite Dimensional Approximation ◽  
Finite Dimensional ◽  
Dimensional Approximation ◽  
Nemytskij Operators ◽  
First Time

This paper focuses on two Dirichlet boundary value problems whose differential operators in the principal part exhibit a lack of ellipticity and contain a convection term (depending on the solution and its gradient). They are driven by a degenerated (p,q)-Laplacian with weights and a competing (p,q)-Laplacian with weights, respectively. The notion of competing (p,q)-Laplacians with weights is considered for the first time. We present existence and approximation results that hold under the same set of hypotheses on the convection term for both problems. The proofs are based on weighted Sobolev spaces, Nemytskij operators, a fixed point argument and finite dimensional approximation. A detailed example illustrates the effective applicability of our results.

Finite-dimensional approximation of the scattering matrix

1986 ◽  
Vol 64 (5) ◽  
pp. 611-616 ◽  
Author(s):  
Helmut Kröger ◽  
Anais Smailagic ◽  
Ralph Girard
Keyword(s):  
Weak Coupling ◽  
Weak Coupling Regime ◽  
S Wave ◽  
Proton Proton ◽  
Time Evolution Operator ◽  
Finite Dimensional Approximation ◽  
Finite Dimensional ◽  
Dimensional Approximation ◽  
S Matrix ◽  
Computer Calculations

A finite-dimensional nonperturbative approximation scheme of the time-evolution operator and the S matrix for relativistic field theories is discussed. It is amenable to computer calculations. Parallels with lattice-field theory are drawn. The method is outlined for the ϕ4 theory. Equivalence to standard perturbation theory in the weak-coupling regime is obtained in the limit of the approximation parameters. The method is tested numerically for nonrelativistic proton–proton s-wave scattering and the the ϕ4 model in the weak-coupling regime in 1 + 1 dimensions. In both examples, convergence to the reference solution is found.

An Approach to Acoustic Noise Control via Passivity Techniques

2001 ◽  
Author(s):  
A. G. Kelkar ◽  
Suresh M. Joshi
Keyword(s):  
Design Methodology ◽  
Controller Design ◽  
Acoustic Noise ◽  
Broad Band ◽  
Resonant Mode ◽  
Robust Controller ◽  
Finite Dimensional Approximation ◽  
Finite Dimensional ◽  
Guaranteed Stability ◽  
Dimensional Approximation

Abstract This paper presents a passivity-based robust controller design methodology for broad-band control of acoustic noise in ducts. A brief review of passivity-based control using passification techniques is given for non-passive dynamic systems. An application of this design technique to the acoustic duct system is presented. The acoustic duct model being inherently non-passive, passification techniques are necessary to render the system passive. The controller design is based on finite-dimensional approximation and is shown to be robust to unmodeled dynamics and parametric uncertainties. The control design methodology exploits inherent robustness of passivity-based controllers and selective mode attenuation capability of resonant mode controllers. The resulting controller is low-order, robust, broadband, and has guaranteed stability.

Inversion of the Initial Value for a Time-Fractional Diffusion-Wave Equation by Boundary Data

2020 ◽  
Vol 20 (1) ◽  
pp. 109-120 ◽  
Author(s):  
Suzhen Jiang ◽  
Kaifang Liao ◽  
Ting Wei
Keyword(s):  
Inverse Problem ◽  
Wave Equation ◽  
Fractional Diffusion ◽  
Initial Value ◽  
Diffusion Wave ◽  
One Dimensional ◽  
Finite Dimensional Approximation ◽  
Finite Dimensional ◽  
Dimensional Approximation ◽  
Continuation Technique

AbstractIn this study, we consider an inverse problem of recovering the initial value for a multi-dimensional time-fractional diffusion-wave equation. By using some additional boundary measured data, the uniqueness of the inverse initial value problem is proven by the Laplace transformation and the analytic continuation technique. The inverse problem is formulated to solve a Tikhonov-type optimization problem by using a finite-dimensional approximation. We test four numerical examples in one-dimensional and two-dimensional cases for verifying the effectiveness of the proposed algorithm.

An Inner/Outer Loop Controller for Rigid-Flexible Manipulators

1992 ◽  
Vol 114 (4) ◽  
pp. 580-587 ◽  
Author(s):  
F. Khorrami ◽  
S. Zheng
Keyword(s):  
Controller Design ◽  
Nonlinear Partial Differential Equation ◽  
Body Motion ◽  
Flexible Manipulators ◽  
Outer Loop ◽  
Finite Dimensional Approximation ◽  
Finite Dimensional ◽  
Dimensional Approximation ◽  
Loop Dynamics ◽  
Control Methodology

In this paper, vibration control of flexible-link manipulators is considered. A nonlinear partial differential equation describing the dynamics of a two-link planar manipulator with a flexible forearm is derived. Thereafter, utilizing the eigenfunctions corresponding to the boundary value problem at hand, a finite-dimensional approximation of the model is given. The controller design strategy is based upon an inner-loop controller which corresponds to the rigid body motion of the manipulator taking into consideration the vibrations of the manipulator and an outer-loop controller for further vibration damping and robustness enhancement of the closed-loop dynamics to parameter variations in the system. The measurement used in the outer-loop controller is obtained through an accelerometer mounted on the flexible forearm which can be easily attained in an experimental setup. The control methodology advocated in this paper are applicable to the multi-link flexible manipulators.

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