scholarly journals GENERALIZED SOLUTION OF A MIXED PROBLEM FOR LINEAR HYPERBOLIC SYSTEM

2014 ◽  
Vol 96 (1) ◽  
Author(s):  
L.S. Chadli ◽  
S. Melliani ◽  
A. Moujahid
Keyword(s):  
Mixed Problem ◽  
Hyperbolic System ◽  
Generalized Solution ◽  
Linear Hyperbolic System

scholarly journals ОN THE QUALITATIVE ANALYSIS OF CERTAIN FLOTATION PROCESSES

2020 ◽  
Vol 9 (11) ◽  
pp. 91-99
Keyword(s):  
Fixed Point ◽  
Qualitative Analysis ◽  
Mixed Problem ◽  
Hyperbolic System ◽  
Transmission Lines ◽  
Generalized Solution ◽  
Fixed Point Method ◽  
Successive Approximations ◽  
First Order ◽  
Operator Form

The present paper is devoted to the qualitative analysis of certain flotation processes describing by a first order hyperbolic system of partial differential equations. The system in question is like telegrapher equations. That is why, we use the methods for examining the transmission lines set out in the papers mentioned in the References. We formulate a mixed problem for this system with boundary conditions corresponding to the processes in the flotation cameras. We present the mixed problem for the hyperbolic system in a suitable operator form and prove an existence of generalized solution by fixed point method. One can obtain an explicit approximated solution as a step in the sequence of successive approximations.

scholarly journals LOSSY TRANSMISSION LINES TERMINATED BY PARALLEL CONNECTED RLC-ELEMENTS WITHOUT THE HEAVISIDE’S CONDITION

2019 ◽  
pp. 1-13
Author(s):  
Vasil G. Angelov
Keyword(s):  
Transmission Line ◽  
Mixed Problem ◽  
Hyperbolic System ◽  
Transmission Lines ◽  
Electromagnetic Waves ◽  
Neutral Type ◽  
Generalized Solution ◽  
Line System ◽  
Lossy Transmission ◽  
Transverse Electromagnetic

The paper deals with analysis of propagation of transverse electromagnetic waves along lossy transmission lines terminated by a circuit consisting of parallel connected RLCelements. Using the Kirchhoff’s laws we derive boundary conditions and formulate the mixed problem for hyperbolic system describing the lossy transmission line. Without the Heaviside's condition, we cannot guarantee the distortionless propagation of waves and hence we cannot apply the known methods. That is why we apply a different method and obtain conditions for existence-uniqueness of generalized solution. We change variables and formulate a mixed problem for the hyperbolic system with respect to the new variables. The nonlinear characteristics of the RLC-elements generate nonlinearity in the equations of neutral type on the boundary. We propose an operator presentation of the mixed problem for transmission line system and by means of fixed point technique we prove existence-uniqueness of a generalized solution.

scholarly journals LOSSY TRANSMISSION LINES TERMINATED BY PARALLEL CONNECTED RLC-ELEMENTS WITHOUT THE HEAVISIDE’S CONDITION

2019 ◽  
pp. 1-13 ◽  
Author(s):  
Vasil G. Angelov
Keyword(s):  
Transmission Line ◽  
Mixed Problem ◽  
Hyperbolic System ◽  
Transmission Lines ◽  
Electromagnetic Waves ◽  
Neutral Type ◽  
Generalized Solution ◽  
Line System ◽  
Lossy Transmission ◽  
Transverse Electromagnetic

The paper deals with analysis of propagation of transverse electromagnetic waves along lossy transmission lines terminated by a circuit consisting of parallel connected RLCelements. Using the Kirchhoff’s laws we derive boundary conditions and formulate the mixed problem for hyperbolic system describing the lossy transmission line. Without the Heaviside's condition, we cannot guarantee the distortionless propagation of waves and hence we cannot apply the known methods. That is why we apply a different method and obtain conditions for existence-uniqueness of generalized solution. We change variables and formulate a mixed problem for the hyperbolic system with respect to the new variables. The nonlinear characteristics of the RLC-elements generate nonlinearity in the equations of neutral type on the boundary. We propose an operator presentation of the mixed problem for transmission line system and by means of fixed point technique we prove existence-uniqueness of a generalized solution.

Classical and generalized of a mixed problem– solutions for a non-homogeneous wave equation

2019 ◽  
Vol 484 (1) ◽  
pp. 18-20
Author(s):  
A. P. Khromov ◽  
V. V. Kornev
Keyword(s):  
Wave Equation ◽  
Fourier Series ◽  
Mixed Problem ◽  
Homogeneous Equation ◽  
Generalized Solution ◽  
Problem Solution ◽  
Homogeneous Wave ◽  
Homogeneous Wave Equation ◽  
Explicit Expressions

This study follows A.N. Krylov’s recommendations on accelerating the convergence of the Fourier series, to obtain explicit expressions of the classical mixed problem–solution for a non-homogeneous equation and explicit expressions of the generalized solution in the case of arbitrary summable functions q(x), ϕ(x), y(x), f(x, t).

Riesz basis of exponential family for a hyperbolic system

2019 ◽  
Vol 25 (1) ◽  
pp. 13-23
Author(s):  
Abdelkader Intissar ◽  
Aref Jeribi ◽  
Ines Walha
Keyword(s):  
Hilbert Space ◽  
Linear System ◽  
Hyperbolic System ◽  
Riesz Basis ◽  
Infinitesimal Generator ◽  
Exponential Family ◽  
Analysis Method ◽  
Spectral Analysis Method ◽  
Weaker Conditions ◽  
Linear Hyperbolic System

Abstract This paper studies a linear hyperbolic system with boundary conditions that was first studied under some weaker conditions in [8, 11]. Problems on the expansion of a semigroup and a criterion for being a Riesz basis are discussed in the present paper. It is shown that the associated linear system is the infinitesimal generator of a {C_{0}} -semigroup; its spectrum consists of zeros of a sine-type function, and its exponential system {\{e^{\lambda_{n}t}\}_{n\geq 1}} constitutes a Riesz basis in {L^{2}[0,T]} . Furthermore, by the spectral analysis method, it is also shown that the linear system has a sequence of eigenvectors, which form a Riesz basis in Hilbert space, and hence the spectrum-determined growth condition is deduced.

Sign in / Sign up

Export Citation Format

Share Document