Wyniki wyszukiwania - BazTech

1

Conditional stability estimate for an ill-posed elliptic equation by using nonlocal conditions

Benrabah Abderafik

Journal of Applied Mathematics and Computational Mechanics

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2022

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Vol. 21, nr 3

5--17

EN

We consider an ill-posed linear homogeneous fourth-order elliptic equation. We show that the problem is ill-posed in the sense of Hadamard, i.e., the solution does not depend continuously on the given data. We propose a regularization method via nonlocal conditions and under some a priori bound assumptions different estimates for the regularized solution are obtained. Numerical examples for a rectangle domain show the effectiveness of the new method in providing highly accurate numerical solutions as the noise level tends to zero.

2

Estimates for a beam-like partial differential operator and applications

Belahdji Meriem, Ayad Setti, Mortad Mohammed Hichem

Journal of Applied Analysis

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2022

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Vol. 28, nr 2

181--188

EN

The aim of this paper is to provide some a priori estimates for a beam-like operator. Some applications and counterexamples are also given.

3

Existence results and a priori estimates for solutions of quasilinear problems with gradient terms

Filippucci Roberta, Lini Chiara

Opuscula Mathematica

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2019

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Vol. 39, no. 2

195--205

EN

In this paper we establish a priori estimates and then an existence theorem of positive solutions for a Dirichlet problem on a bounded smooth domain in [formula] with a nonlinearity involving gradient terms. The existence result is proved with no use of a Liouviiie theorem for the limit problem obtained via the usual blow up method, in particular we refer to the modified version by Ruiz. In particular our existence theorem extends a result by Lorca and Ubilla in two directions, namely by considering a nonlinearity which includes in the gradient term a power of u and by removing the growth condition for the nonlinearity ∫ at u = 0.

4

Fractional flow formulation for three-phase non-isothermal flow in porous media

Wójcik W., Temirbekov N., Baigereyev D.

Przegląd Elektrotechniczny

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2016

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R. 92, nr 7

24--31

EN

The present paper focuses on the simulation of three-phase non-isothermal compressible flow in porous media taking into account capillary effects. We propose a new formulation of the considered non-isothermal problem in which the gradients of capillary pressure functions are eliminated from the pressure and temperature equations by the introduction of a change of variables for the pressure. The mentioned change of variables is referred to as the global pressure. A computational algorithm for the numerical implementation of the problem using the finite difference method is proposed. A priori estimate for the solution of the difference problem is obtained. The results of numerical experiments on the example of a one-dimensional problem are presented.

PL

W pracy autorzy koncentrują się na symulacji trójfazowego nie izotermicznego ściśliwego przepływu w środowiskach porowatych przy uwzględnieniu efektów kapilarnych. Zaproponowano nowe sformułowanie zagadnienia w którym gradienty funkcji ciśnienia kapilarnego są wyeliminowane z równań ciśnienia i temperatury poprzez zamiane zmiennych dla ciśnienia globalnego. Zaproponowano implementację algorytmu wykorzystując schemat różnicowy. Wyniki obliczeń dla jednowymiarowego zagadnienia przedstawiono w zakończeniu pracy.

5

Classical solutions of mixed problems for quasilinear first order PFDEs on a cylindrical domain

Czernous W.

Opuscula Mathematica

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2014

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Vol. 34, no. 2

291--310

EN

We abandon the setting of the domain as a Cartesian product of real intervals, customary for first order PFDEs (partial functional differential equations) with initial boundary conditions. We give a new set of conditions on the possibly unbounded domain Ω with Lipschitz differentiable boundary. Well-posedness is then reliant on a variant of the normal vector condition. There is a neighbourhood of ∂Ω with the property that if a characteristic trajectory has a point therein, then its every earlier point lies there as well. With local assumptions on coefficients and on the free term, we prove existence and Lipschitz dependence on data of classical solutions on (0,c)×Ω to the initial boundary value problem, for small c. Regularity of solutions matches this domain, and the proof uses the Banach fixed-point theorem. Our general model of functional dependence covers problems with deviating arguments and integro-differential equations.