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1
Content available remote Strangely sweeping one-dimensional diffusion
100%
Rudnicki R.
|
1993
|
tom 58
|
nr 1
37-45
EN
Let X(t) be a diffusion process satisfying the stochastic differential equation dX(t) = a(X(t))dW(t) + b(X(t))dt. We analyse the asymptotic behaviour of p(t) = Prob{X(t) ≥ 0} as t → ∞ and construct an equation such that $lim sup_{t→∞} t^{-1} ∫_0^t p(s) ds = 1$ and $lim inf_{t→∞}t^{-1} ∫_0^t p(s) ds = 0$.
2
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.
3
Content available On the Tonelli method for the degenerate parabolic Cauchy problem with functional argument
80%
Topolski K. A.
|
2014
|
tom Vol. 34, no. 2
425--441
EN
The degenerate parabolic Cauchy problem is considered. A functional argument in the equation is of the Hale type. As a limit of piecewise classical solutions we obtain a viscosity solution of the main problem. Presented method is an adaptation of Tonelli's constructive method to the partial differential-functional equation. It is also shown that this approach can be improved by the vanishing viscosity method and regularisation process.
4
Content available remote The representation of smooth functions in terms of the fundamental solution of a linear parabolic equation
80%
Watson N. A.
|
2000
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tom 75
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nr 3
281-287
EN
Let L be a second order, linear, parabolic partial differential operator, with bounded Hölder continuous coefficients, defined on the closure of the strip $X = ℝ^{n} × ]0,a[$. We prove a representation theorem for an arbitrary $C^{2,1}$ function, in terms of the fundamental solution of the equation Lu=0. Such a theorem was proved in an earlier paper for a parabolic operator in divergence form with $C^{∞}$ coefficients, but here much weaker conditions suffice. Some consequences of the representation theorem, for the solutions of Lu=0, are also presented.
5
Content available remote On the classical solutions for parabolic differential - functional Cauchy problem
80%
Topolski K. A.
Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
|
2004
|
tom Vol. 44, nr 2
217-226
EN
We consider the initial value problem for second order differential - functional parabolic equation. Functional dependence is of the Hale type. On the basis of differential inequalities and fixed point method we prove the existence theorem for classical solution. Our formulation covers a large group of nonlocal problems such as , integro-differential equations, and "retarded and deviated" argument. We put particular stress on the last one, as it requires more general treatment.
6
Content available remote The $L^p$ solvability of the Dirichlet problems for parabolic equations
80%
Tao X. X.
Studia Mathematica
|
2000
|
tom 139
|
nr 1
69-80
EN
For two general second order parabolic equations in divergence form in Lip(1,1/2) cylinders, we give a criterion for the preservation of $L^p$ solvability of the Dirichlet problems.
7
Generalization of maximum principle
80%
Jama D.
Zeszyty Naukowe. Matematyka - Fizyka / Politechnika Śląska
|
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.
8
Content available General dynamic projecting of maxwell equations
70%
Wojda P. , Leble S.
TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk
|
2017
|
tom Vol. 21, No 2
85--96
EN
A complete – system of Maxwell equations is splitting into independent subsystems by means of a special dynamic projecting technique. The technique relies upon a direct link between field components that determine correspondent subspaces. The explicit form of links and corresponding subspace evolution equations are obtained in conditions of certain symmetry, it is illustrated by examples of spherical and quasi-one-dimensional waves.
9
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.
10
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.
11
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
|
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.
12
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
|
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.
13
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.
14
Content available On properties of minimizers of a control problem with time-distributed functional related to parabolic equations
60%
Astashova I. V. , Filinovskiy A. V.
Opuscula Mathematica
|
2019
|
tom Vol. 39, no. 5
595--609
EN
We consider a control problem given by a mathematical model of the temperature control in industrial hothouses. The model is based on one-dimensional parabolic equations with variable coefficients. The optimal control is defined as a minimizer of a quadratic cost functional. We describe qualitative properties of this minimizer, study the structure of the set of accessible temperature functions, and prove the dense controllability for some set of control functions.
15
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.
16
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.
17
Content available remote The radial solution of the heat equation in the cylindrical ring
41%
Koroński J.
Fasciculi Mathematici
|
2010
|
tom 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.
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