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1
On the positive solutions of a parabolic equation
100%
Jama D. , Czech R. , Szopa M. , Wituła R.
Zeszyty Naukowe. Matematyka - Fizyka / Politechnika Śląska
|
2010
|
tom 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.
2
Generalization of maximum principle
80%
Jama D.
Zeszyty Naukowe. Matematyka - Fizyka / Politechnika Śląska
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2010
|
tom 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.
3
Content available remote Difference methods for infinite systems of quasilinear parabolic functional differential equations
80%
Jaruszewska-Walczak D.
|
2010
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tom 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.
4
Numeryczne rozwiązanie kwaziliniowego zagadnienia początkowo-brzegowego dla równania typu parabolicznego
80%
Boychuk V.
Zeszyty Naukowe. Matematyka / Politechnika Opolska
|
2001
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tom 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.
5
Content available remote The radial solution of the factorised polyparabolic equation in spherical shall
70%
Koroński J.
Fasciculi Mathematici
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1999
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tom 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.
6
Content available remote The periodic solution to biparabolic equation for the three-dimensional temporal-spatial cylinder with boundary conditions of Riquier type
70%
Koroński J.
Fasciculi Mathematici
|
1999
|
tom Nr 30
71-79
EN
In this paper we shaII construct the periodic solution for biparabolic f equation in cylindrical domain with boundary conditions of Riguier type. To construct the solution we shaII apply the convenient heat biparabolic potentials ! with unkow densities and biparabolic potential ofthe source function. To detern1ine these densities we shaII apply the suitable system of integral equations. The periodic solution is a sum of periodic boundary potentials and periodic biparabolic potential ofthe source function.
7
Content available Input reconstruction by feedback control for the Schlögl and FitzHugh–Nagumo equations
60%
Maksimov V. , Trlötzsch F.
International Journal of Applied Mathematics and Computer Science
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2020
|
tom 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.
8
Content available remote On the periodic solution of the parabolic problem for the cylinder
60%
Koroński J.
Fasciculi Mathematici
|
1999
|
tom Nr 30
63-70
EN
The subject ofthe paper is a construction of an explicit periodic solution ofthe parabolic problem for the cylinder. To construct of the periodic solution we shall apply the convenient Green function. In this paper the theorems on uniqueness and existence of solution of considered ( l) -(2) problem is given.
9
Content available remote A limit problem for a factorised parabolic equation of the fourth order
60%
Pieniążek A.
Fasciculi Mathematici
|
1999
|
tom Nr 30
131-146
EN
The aim of this paper is the construction of the classical solution to a nonlinear factorised differential biparabolic equation of the fourth order, in a rectangular domain, with boundary-value conditions ofthe Dirichlet and the Neurnann types.
10
Content available remote On convergence of explicit finite volume scheme for one-dimensional three-component two-phase flow model in porous media
60%
Mostefai M. L. , Choucha A. , Cherif B.
|
|
tom 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.
11
Content available remote On the unbounded solutions for parabolic differential-functional Cauchy problem
60%
Topolski K.
|
2007
|
tom 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.
12
Content available remote Modelling a solution of a homogeneous parabolic equation with random initial condition from Lp(Ω)
60%
Kuchinka K. , Slyvka-Tylyshchak G.
Przegląd Elektrotechniczny
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2023
|
tom 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.
13
Content available remote A mixed problem for a parabolic equation of higher order with integral conditions
60%
Mesloub S. , Mezhoudi R. , Medjeden M.
Bulletin of the Polish Academy of Sciences. Mathematics
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2002
|
tom 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.
14
Content available On an algorithm for the problem of tracking a trajectory of a parabolic equation
60%
Blizorukova M. , Maksimov V.
|
|
tom 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.
15
Silnie zaburzone równanie typu parabolicznego z nielokalnym warunkim względem czasowej zmiennej
60%
Flyud V. , Tsymbal V.
Zeszyty Naukowe. Matematyka / Politechnika Opolska
|
2001
|
tom 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.
16
Content available remote General decay for a nonlinear pseudo-parabolic equation with viscoelastic term
51%
Vu N. T. , Dung D. B. , Dung H. T. H.
Demonstratio Mathematica
|
2022
|
tom 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.
17
Content available remote Optimality conditions for state-constrained PDE control problems with time-dependent controls
51%
Los Reyes J. C. d. , Merino P. , Rehberg F. , Troltzsch F.
Control and Cybernetics
|
2008
|
tom 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.
18
Content available remote Notes on continuity result for conformable diffusion equation on the sphere: the linear case
51%
Nguyen V. T.
Demonstratio Mathematica
|
2022
|
tom 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.
19
Content available remote Solving Parabolic Equations by Using the Method of Fast Convergent Iterations
51%
Bondarenko V. , Bidyuk P. , Bernatska J.
International Journal of Applied Mathematics and Computer Science
|
2000
|
tom 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 Source localization and sensor placement in environmental monitoring
41%
Khapalov A.
International Journal of Applied Mathematics and Computer Science
|
2010
|
tom 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.
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