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1
Content available remote Stability of difference equations generated by parabolic differential functional equations
Ciarski R.
Demonstratio Mathematica
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2005
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Vol. 38, nr 1
101--117
EN
The aim of this paper is to present a numerical approximation for the initial boundary value problem for quasilinear parabolic differential functional equations. The convergence result is proved for the difference scheme with the property that the difference operators approximating mixed derivatives depend on local properties of coefficients of the differential equation. A numerical example is given.
2
Content available remote Different variants of the boundary element method for parabolic equations
Majchrzak E., Ładyga E., Mendakiewicz J., Piasecka Belkhayat A.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2004
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Vol. 3, nr 1
127--132
EN
In the paper the different algorithms of boundary element method for parabolic equation are presented, this means the 1st and 2nd scheme of the BEM, the BEM using discretization in time and the BEM using Laplace transform.
3
Content available remote Dynamically equivalent perturbations of linear parabolic equations
Czaja R.
Demonstratio Mathematica
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2004
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Vol. 37, nr 2
327--348
EN
A family of abstract parabolic equations with sectorial operator is studied in this paper. The conditions are provided to show that the global attractors for each equation exist and coincide. Although the common dynamics is simple, the examples presented in the final part of the paper indicate that the considered family may contain a linear equation together with a large number of its nonlinear perturbations. The mentioned examples include both scalar second order equations and the celebrated Cahn-Hilliard system.
4
Content available remote Smoothing effect in semilinear parabolic equations
Napiórkowska J.
Demonstratio Mathematica
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2003
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Vol. 36, nr 2
355--368
EN
The purpose of this paper is to describe the smoothness of solutions of semilinear parabolic equations with 2m-th order elliptic operator. Similar result for second order equations was given e.g. by F. Rothe [RO] under the name of "bootstrap" and "feedback".
5
The existence and uniqueness of solution of one coupled plate thermomechanics problem
Krysko V. A., Awrejcewicz J., Bruk V. M.
Journal of Applied Analysis
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2002
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Vol. 8, nr 1
129-139
EN
The thermo-elastic plate system of equations is analysed. The sufficient conditions of existence, uniqueness and continuity dependence on initial data of the Cauchy problem solutions for differential-operational equation of mixed type (a part of the equation of hyperbolic type, and a part of parabolic type) are given in this paper. If the operational coefficients are suitably chosen, the investigated equation can be used to obtain a differential equation describing vibrations of a plate — the modified Germain-Lagrange equation of hyperbolic type. Moreover, in order to define the temperature field, one can use a three-dimensional equation of thermal conductivity (a parabolic equation).
6
Content available remote Nonlinear singular difference inequalities suitable for discretizations of parabolic equations
Medved M.
Demonstratio Mathematica
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2000
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Vol. 33, nr 3
517-525
EN
In this paper we solve a nonlinear, singular difference inequality which is a discrete version of generalized integral inequalities of Henry-Gronwall type and their Bihari nonlinear version.
7
Oscillation criteria for a class of functional parabolic equations
Kusano T., Yoshida N.
Journal of Applied Analysis
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1999
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Vol. 5, nr 1
1-16
EN
Oscillations of parabolic equations with functional arguments are studied, and sufficient conditions are derived for all solutions of certain boundary value problems to be oscillatory in a cylindrical domain. Our approach is to reduce the multidimensional problems to one-dimensional problems for functional differential inequalities.
8
Content available Analysis of the Lagrange-SQP-Newton method for the control of a phase field equation
Heinkenschloss M., Troeltzsch F.
Control and Cybernetics
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1999
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Vol. 28, no 2
177-211
EN
This paper investigates the local convergence of the Lagrange-SQP-Newton method applied to an optimal control problem governed by a phase field equation with distributed control. The phase field equation is a system of two semilinear parabolic differential equations. Stability analysis of optimization problems and regularity results for parabolic differential equations are used to proof convergence of the controls with respect to the L[sup 2](Q) norm and with respect to the L[sup infinity](Q) norm.
9
Content available remote Oscillations of systems of neutral delay parabolic equations
Li W., Cui B.
Demonstratio Mathematica
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1998
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Vol. 31, nr 4
813-824
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