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1
Content available remote Modelling a solution of a homogeneous parabolic equation with random initial condition from Lp(Ω)
Kuchinka Katalin, Slyvka-Tylyshchak Ganna
Przegląd Elektrotechniczny
|
2023
|
R. 99, nr 5
77--82
EN
In this paper, a model of solutions to the heat equation with initial conditions from the Orlicz space Lp(Ω) of random variables is built. The constructed model approximates the solution of a homogeneous parabolic equation with given reliability and accuracy in some Orlicz space.
PL
W pracy zbudowano model rozwiązan równania ciepła z warunkami początkowymi z przestrzeni Orlicza Lp(Ω) zmiennych losowych. Skonstruowany model przybliza rozwiązanie jednorodnego równania parabolicznego z zadaną niezawodnoscią i dokładnoscią w pewnej przestrzeni Orlicza.
2
Ocena efektywności generacji map tłumienia propagacyjnego
Kryk Michał
Przegląd Telekomunikacyjny + Wiadomości Telekomunikacyjne
|
2022
|
nr 4
519--522
PL
Nowoczesne systemy komunikacji bezprzewodowej wykorzystują różne rozwiązania technologiczne w celu zwiększenia wydajności tworzonych sieci radiowych. Obecnie jednym z kierunków pozwalających usprawnić zarządzanie zasobami radiowymi jest wykorzystanie mapy środowiska radiowego (REM). REM są coraz częściej wykorzystywane w mobilnych sieciach doraźnych (MANET), w szczególności w taktycznych sieciach wojskowych. Mapy tłumienia propagacyjnego (PAM) są kluczowymi elementami REM, które pozwalają na określenie zasięgów węzłów sieci radiowej. W niniejszym artykule zostanie przedstawiona ocena efektywności autorskiego algorytmu generowania PAM. Zaproponowany algorytm PAM bazuje na metodzie równań parabolicznych (PEM), interpolacji liniowej oraz profilach terenu wyznaczanych na podstawie map wysokościowych DTED.
EN
Modern wireless communication systems use various technological solutions to increase the efficiency of the created radio networks. Currently, the use of the radio environment map (REM) is one of the directions allowing improvement of radio resource management. REM is being used more often in emerging mobile ad-hoc networks (MANETs), in particular in tactical military networks. Propagation attenuation maps (PAMs) are the key elements of REM in determining the ranges of the radio network nodes. In this paper, an efficiency assessment of PAM generation is presented. The proposed PAM algorithm is based on the parabolic equation method (PEM), linear interpolation, and terrain profiles determined based on the DTED elevation maps.
3
Content available remote Notes on continuity result for conformable diffusion equation on the sphere: the linear case
Nguyen Van Tien
Demonstratio Mathematica
|
2022
|
Vol. 55, nr 1
952--962
EN
In this article, we are interested in the linear conformable diffusion equation on the sphere. Our main goal is to establish some results on the continuity problem with respect to fractional order. The main technique is based on several evaluations on the sphere using spherical basis functions. To overcome the difficulty, we also need to use some calculations to control the generalized integrals.
4
Content available remote General decay for a nonlinear pseudo-parabolic equation with viscoelastic term
Vu Ngo Tran, Dung Dao Bao, Dung Huynh Thi Hoang
Demonstratio Mathematica
|
2022
|
Vol. 55, nr 1
737--751
EN
This work is concerned with a multi-dimensional viscoelastic pseudo-parabolic equation with critical Sobolev exponent. First, with some suitable conditions, we prove that the weak solution exists globally. Next, we show that the stability of the system holds for a much larger class of kernels than the ones considered in previous literature. More precisely, we consider the kernel g:[0,∞)⟶(0,∞) satisfying g′(t)⩽−ξ(t)G(g(t)) , where ξ and G are functions satisfying some specific properties.
5
Content available remote On convergence of explicit finite volume scheme for one-dimensional three-component two-phase flow model in porous media
Mostefai Mohamed Lamine, Choucha Abdelbaki, Cherif Bahri
Demonstratio Mathematica
|
2021
|
Vol. 54, nr 1
510--526
EN
In this work, we develop and analyze an explicit finite volume scheme for a one-dimensional nonlinear, degenerate, convection–diffusion equation having application in petroleum reservoir. The main difficulty is that the solution typically lacks regularity due to the degenerate nonlinear diffusion term. We analyze a numerical scheme corresponding to explicit discretization of the diffusion term and a Godunov scheme for the advection term. L∞ stability under appropriate CFL conditions and BV estimates are obtained. It is shown that the scheme satisfies a discrete maximum principle. Then we prove convergence of the approximate solution to the weak solution of the problem, and we mount convergence results to a weak solution of the problem in L1 . Results of numerical experiments are presented to validate the theoretical analysis.
6
Content available Input reconstruction by feedback control for the Schlögl and FitzHugh–Nagumo equations
Maksimov Vyacheslav, Trlötzsch Fredi
International Journal of Applied Mathematics and Computer Science
|
2020
|
Vol. 30, no. 1
5--22
EN
Dynamical reconstruction of unknown time-varying controls from inexact measurements of the state function is investigated for a semilinear parabolic equation with memory. This system includes as particular cases the Schlögl model and the FitzHugh–Nagumo equations. A numerical method is suggested that is based on techniques of feedback control. An error analysis is performed. Numerical examples confirm the theoretical predictions.
7
Content available On an algorithm for the problem of tracking a trajectory of a parabolic equation
Blizorukova M., Maksimov V.
International Journal of Applied Mathematics and Computer Science
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2017
|
Vol. 27, no. 3
457--465
EN
In this paper, we consider the problem of tracking a solution of a reference parabolic equation by a solution of another equation. A stable algorithm based on the extremal shift method is proposed for this problem. The algorithm is designed to work on a sufficiently large time interval where both equations operate.
8
On the positive solutions of a parabolic equation
Jama D., Czech R., Szopa M., Wituła R.
Zeszyty Naukowe. Matematyka - Fizyka / Politechnika Śląska
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2010
|
z. 92
7-11
EN
In this paper positive solutions of some weak nonlinear parabolic equations were investigated. Two theorems were proved. One for positive solutions and another includes a prior estimation.
9
Generalization of maximum principle
Jama D.
Zeszyty Naukowe. Matematyka - Fizyka / Politechnika Śląska
|
2010
|
z. 92
13-19
PL
Celem pracy jest otrzymanie zasady maksimum dla słabo nieliniowego równania parabolicznego, określonego w n+1 wymiarowym walcu. Rozważane są klasyczne rozwiązania rozpatrywanego rownania.
EN
The paper presents maximum principle for weak nonlinear parabolic equation defined in n + 1 dimensional cylinder. Only classical solutions were taken into consideration.
10
Content available remote Source localization and sensor placement in environmental monitoring
Khapalov A.
International Journal of Applied Mathematics and Computer Science
|
2010
|
Vol. 20, no 3
445-458
EN
In this paper we discuss two closely related problems arising in environmental monitoring. The first is the source localization problem linked to the question How can one find an unknown 'contamination source'? The second is an associated sensor placement problem: Where should we place sensors that are capable of providing the necessary 'adequate data' for that? Our approach is based on some concepts and ideas developed in mathematical control theory of partial differential equations.
11
Content available remote The radial solution of the heat equation in the cylindrical ring
Koroński J.
Fasciculi Mathematici
|
2010
|
Nr 43
69-83
EN
The subject of the paper is the construction of a solution to the parabolic problem for the cylindrical ring with initial condition of Cauchy type and boundary conditions of Dirichlet type. To construct the radial solution we do not use the Bessel functions but we apply the convenient Green function, heat potentials and Banach fixed point theorem.
12
Content available remote Difference methods for infinite systems of quasilinear parabolic functional differential equations
Jaruszewska-Walczak D.
Demonstratio Mathematica
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2010
|
Vol. 43, nr 1
213-230
EN
Classical solutions of initial boundary value problems for infinite systems of quasilinear parabolic differential functional equations are considered. Two type of difference schemes are constructed. We prove that solutions of infinite difference schemes approximate solutions of our differential functional problem. In the second part of the paper we show that solutions of infinite differential functional systems can be approximated by solutions of difference systems with initial boundary conditions and the systems are finite. A complete convergence analysis for the methods is presented. The proof of the stability is based on a comparison technique with nonlinear estimates of the Perron type for given functions.
13
Content available remote Optimality conditions for state-constrained PDE control problems with time-dependent controls
Los Reyes J. C. de, Merino P., Rehberg F., Troltzsch F.
Control and Cybernetics
|
2008
|
Vol. 37, no 1
5-38
EN
The paper deals with optimal control problems for semilinear elliptic and parabolic PDEs subject to pointwise state constraints. The main issue is that the controls are taken from a restricted control space. In the parabolic case, they are Rm -vector-valued functions of time, while they are vectors of Rm in elliptic problems. Under natural assumptions, first- and second-order sufficient optimality conditions are derived. The main result is the extension of second-order sufficient conditions to semilinear parabolic equations in domains of arbitrary dimension. In the elliptic case, the problems can be handled by known results of semi-infinite optimization. Here, different examples are discussed that exhibit different forms of active sets and where second-order sufficient conditions are satisfied at the optimal solution.
14
Content available remote On the unbounded solutions for parabolic differential-functional Cauchy problem
Topolski K.
Demonstratio Mathematica
|
2007
|
Vol. 40, nr 1
151-160
EN
We consider the initial value problem for second order differential–func- tional equation. Functional dependence on an unknown function is of the Hale type. We prove the existence theorem for unbounded classical solution. Our formulation admits a large group of nonlocal problems. We put particular stress on “retarded and deviated” argument as it seems to be the most difficult.
15
Fractional derivative analysis of Helmholtz and paraxial-wave equations
Turski A. J., Atamaniuk B., Turska E.
Journal of Technical Physics
|
2003
|
Vol. 44, no 2
193-206
EN
Fundamental rules and definitions of Fractional Calculus are outlined. Factorizing 1-D and 2-D Helmholtz equations, four semi-differential eigenfunctions are determined. The functions exhibit incident and reHected plane waves as well as diffracted incident and reflected waves on the half-plane edge. They allow to construct the Sommerfeld half-plane diffraction solutions. Parabolic-Wave Equation (PWE, Leontovich-Fock) for paraxial propagation is factorized and differential fractional solutions of Fresnel-integral type are determined. We arrived at two solutions, which are the mothers of known and new solutions.
16
Content available remote A mixed problem for a parabolic equation of higher order with integral conditions
Mesloub S., Mezhoudi R., Medjeden M.
Bulletin of the Polish Academy of Sciences. Mathematics
|
2002
|
Vol. 50, no 3
313-322
EN
In this paper, we investigate the solvability of a mixed problem with integral conditions for a parabolic equation of higher order. The existence and uniqueness of the strong solution are established with the help of a priori bound and the density of the image of the operator generated by the problem in consideration.
17
Silnie zaburzone równanie typu parabolicznego z nielokalnym warunkim względem czasowej zmiennej
Flyud V., Tsymbal V.
Zeszyty Naukowe. Matematyka / Politechnika Opolska
|
2001
|
z. 17
25-29
PL
Metodą warstwy brzegowej zbudowano asymptotyczne rozwinięcie rozwiązania silnie zaburzonego nielokalnego zagadnienia dla n - wymiarowego równania parabolicznego.
EN
By the boundary layer method an asymptotic expansion of the solution of nonlocal problem to parabolic second order equation with a small parameter multiplying the first order time derivative term is obtained.
18
Numeryczne rozwiązanie kwaziliniowego zagadnienia początkowo-brzegowego dla równania typu parabolicznego
Boychuk V.
Zeszyty Naukowe. Matematyka / Politechnika Opolska
|
2001
|
z. 17
113-118
PL
W artykule rozważano numeryczne rozwiązanie niestacjonarnego kwaziliniowego zagadnienia brzegowego typu parabolicznego. Zaproponowano algorytm rozwiązywania i podano wyniki przykładowych obliczeń.
EN
Numerical solution for non-stationary quasi-linearly parabolic initial-boundary-valued problem is considered. Algorithm for its solution and some results of calculations are presented.
19
Content available remote Solving Parabolic Equations by Using the Method of Fast Convergent Iterations
Bondarenko V., Bidyuk P., Bernatska J.
International Journal of Applied Mathematics and Computer Science
|
2000
|
Vol. 10, no 2
333-344
EN
The paper describes an approach to solving parabolic partial differential equations that generalizes the well-known parametrix method. The iteration technique proposed exhibits faster convergence than the classical parametrix approach. A solution is constructed on a manifold with the application of the Laplace-Beltrami operator. A theorem is formulated and proved to provide a basis for finding a unique solution. Simulation results illustrate the superiority of the proposed approach in comparison with the classical parametrix method.
20
Content available remote The radial solution of the factorised polyparabolic equation in spherical shall
Koroński J.
Fasciculi Mathematici
|
1999
|
Nr 30
81-97
EN
The subject of the paper is a construction of an explicit radial solution of the factorised polyparabolic equation in spherical shall. In this paper the theorems on uniqueness and existence of solution of considered of(l) -(4) problem is given.
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