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1
Content available remote

On boundary-value problems for partial differential equations of order higher than two

100%
Popiołek J.
Annales Polonici Mathematici
|
1996-1997
|
tom 65
|
nr 2
139-150
EN
We prove the existence of solutions of some boundary-value problems for partial differential equations of order higher than two. The general idea is similar to that in [1]. We make an essential use of the results of our paper [12].
2
Content available remote

Properties of some integrals related to partial differential equations of order higher than two

100%
Popiołek J.
Annales Polonici Mathematici
|
1996-1997
|
tom 65
|
nr 2
129-138
EN
We construct fundamental solutions of some partial differential equations of order higher than two and examine properties of these solutions and of some related integrals. The results will be used in our next paper concerning boundary-value problems for these equations.
3
Content available remote

Markov operators: applications to diffusion processes and population dynamics

100%
Rudnicki R.
Applicationes Mathematicae
|
2000
|
tom 27
|
nr 1
67-79
EN
This note contains a survey of recent results concerning asymptotic properties of Markov operators and semigroups. Some biological and physical applications are given.
4
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A general transfer function representation for a class of hyperbolic distributed parameter systems

88%
Bartecki K.
International Journal of Applied Mathematics and Computer Science
|
2013
|
tom 23
|
nr 2
291-307
EN
Results of transfer function analysis for a class of distributed parameter systems described by dissipative hyperbolic partial differential equations defined on a one-dimensional spatial domain are presented. For the case of two boundary inputs, the closed-form expressions for the individual elements of the 2×2 transfer function matrix are derived both in the exponential and in the hyperbolic form, based on the decoupled canonical representation of the system. Some important properties of the transfer functions considered are pointed out based on the existing results of semigroup theory. The influence of the location of the boundary inputs on the transfer function representation is demonstrated. The pole-zero as well as frequency response analyses are also performed. The discussion is illustrated with a practical example of a shell and tube heat exchanger operating in parallel- and countercurrent-flow modes.
5
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On stabilizability of evolution systems of partial differential equations on ℝn×[0,+∞) by time-delayed feedback controlsby time-delayed feedback controls

63%
Fardigola L.
Open Mathematics
|
2003
|
tom 1
|
nr 2
141-156
EN
In this work we obtain sufficient conditions for stabilizability by time-delayed feedback controls for the system $$\frac{{\partial w\left( {x,t} \right)}}{{\partial t}} = A(D_x )w(x,t) - A(D_x )u(x,t), x \in \mathbb{R}^n , t > h, $$ where D x=(-i∂/∂x 1,...-i∂/∂x n), A(σ) and B(σ) are polynomial matrices (m×m), det B(σ)≡0 on ℝn, w is an unknown function, u(·,t)=P(D x)w(·,t−h) is a control, h>0. Here P is an infinite differentiable matrix (m×m), and the norm of each of its derivatives does not exceed Γ(1+|σ|2)γ for some Γ, γ∈ℝ depending on the order of this derivative. Necessary conditions for stabilizability of this system are also obtained. In particular, we study the stabilizability problem for the systems corresponding to the telegraph equation, the wave equation, the heat equation, the Schrödinger equation and another model equation. To obtain these results we use the Fourier transform method, the Lojasiewicz inequality and the Tarski-Seidenberg theorem and its corollaries. To choose an appropriate P and stabilize this system, we also prove some estimates of the real parts of the zeros of the quasipolynomial det {Iλ-A(σ)+B(σ)P(σ)e -hλ.
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