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Wyświetlanie 1-15 z 26
Tytuł:
Existence of the fundamental solution of a second order evolution equation
Autorzy:
Bochenek, Jan
Powiązania:
https://bibliotekanauki.pl/articles/1294733.pdf
Data publikacji:
1997
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
evolution problem
stable family of operators
stable approximations of the evolution operator
fundamental solution
Cauchy problem
uniformly correct Cauchy problem
Opis:
We give sufficient conditions for the existence of the fundamental solution of a second order evolution equation. The proof is based on stable approximations of an operator A(t) by a sequence ${A_n(t)}$ of bounded operators.
Źródło:
Annales Polonici Mathematici; 1997, 66, 1; 15-35
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On interaction between damage growth and material stiffness in 3D structures
Autorzy:
Mika, P.
Powiązania:
https://bibliotekanauki.pl/articles/279694.pdf
Data publikacji:
1999
Wydawca:
Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
Tematy:
damage mechanics
evolution equation
material stiffness
Opis:
Deterioration of material properties; such as, rupture toughness, strength, and rigidity as well as lifetime reductions are modelled by a symmetric second order damage tensor introduced into the constitutive description, when employing the theory of tensor function representations. The growth of damage and state failure are described by a one parameter model of damage evolution and a three parameter failure criterion. The constitutive description for different modes of failure frontpropagation is of particular interest in this study. The comparision between solutions obtained by means of two different physical models; i.e., the linear elastic and linear elastic with damages ones, respectively, has been presented. In both cases the stress redistribution due to geometrrical changes of the structure induced by the crack propagation has been considered. Numerical calculations have been made employing the ABAQUS programme, Runge--Kutta procedures for integrationof the evolution equations, standard methods of matrix division in LU decomposition and Gauss method for solving the set of linear equations.
Procesy degradacji własności materiału, takich jak wytrzymałość, sztywność i redukcja czasu twrałości są modelowane przez symetryczny tensor uszkodzeń drugiego rzędu wprowadzony do opisu konstytutywnego z zastosowaniem teorii reprezentacji funkcji tensorowych. Wzrost uszkodzeń oraz stan zniszczenia są opisywane przez jednoparametrowe równanie evolucji oraz trójparametrowe kryterium zniszczenia. W pracy przedstawiono różne formy propagacji frontu zniszczenia w odniesieniu do opisu konstytutywnego. W tym kontekście dokonano porównania rozwiązań otrzymanych z zastosowaniem dwu odmiennych modeli fizycznych: liniowo sprężystego i liniowo sprężystego z uszkodzeniami. W obydwu przypadkach rozważana jest redystrybucja naprężeń spowodowana zmianami geometrycznymi konstrukcji wywołanymi propagacją zarysowań. W obliczeniach numerycznych odwołano się do programu ABAQUS, procedur Rungego--Kutty w całkowaniu równania ewolucji oraz standardowych metod rozkładu macierzy na górno-- i dolno--trójkątną, a w zakresie rozwiązywania układu równań algebraicznych -- do metody Gaussa.
Źródło:
Journal of Theoretical and Applied Mechanics; 1999, 4; 755-778
1429-2955
Pojawia się w:
Journal of Theoretical and Applied Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On Penna model of population evolution
Autorzy:
Magdoń-Maksymowicz, M.
Powiązania:
https://bibliotekanauki.pl/articles/1941717.pdf
Data publikacji:
2000
Wydawca:
Politechnika Gdańska
Tematy:
population evolution
biological ageining
Penna model
bad mutations
migration process
logistic equation
Gompertz law
Opis:
Computer studies of population evolution are presented. Numerical calculations are based on the Penna model. This model accounts for mutation load of individuals resulting in non-trivial age (a) dependence of the mortality rate q(a) which may be compared with empirical data. The Penna model is also very flexible for suitable modifications of the population evolution process such as hunting, genetic death, migration etc. Here we present some examples of the population growth for different evolution rules. Calculations require about 100 MB memory for 10/sup 6/ population which is necessary to get reliable statistics. The typical running time for 3000 iteration steps is several hours for a HP S2000 machine.
Źródło:
TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk; 2000, 4, 1; 5-18
1428-6394
Pojawia się w:
TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Optimal control of nonlinear evolution equations
Autorzy:
Papageorgiou, Nikolaos
Yannakakis, Nikolaos
Powiązania:
https://bibliotekanauki.pl/articles/729352.pdf
Data publikacji:
2001
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
evolution triple
compact embedding
monotone operator
pseudomonotone operator
L-generalized pseudomonotonicity
integration by parts
evolution inclusion
saddle point
necessary conditions
adjoint equation
distributed parameter systems
Opis:
In this paper, first we consider parametric control systems driven by nonlinear evolution equations defined on an evolution triple of spaces. The parametres are time-varying probability measures (Young measures) defined on a compact metric space. The appropriate optimization problem is a minimax control problem, in which the system analyst minimizes the maximum cost (risk). Under general hypotheses on the data we establish the existence of optimal controls.
Then we pass to nonparametric systems, which are governed by nonlinear evolution equations with nonmonotone operators. We prove two existence results for such evolution inclusions, which are of independent interest and extend significantly the results existing in the literature. Then we solve time-optimal and Meyer-type optimization problems. In Section 5, we derive necessary conditions for saddle point optimality in the minimax control problem. We conclude the paper with three examples of distributed parameter control systems.
Źródło:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2001, 21, 1; 5-50
1509-9407
Pojawia się w:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The identification of the boundary geometry with corner points in inverse two-dimensional potential problems
Autorzy:
Zieniuk, E.
Gabrel, W.
Powiązania:
https://bibliotekanauki.pl/articles/1931586.pdf
Data publikacji:
2002
Wydawca:
Politechnika Gdańska
Tematy:
inverse boundary value problem
boundary geometry identification
geometry
parametric integral equation system
finite element method
boundary element method
evolution algorithm
genetic algorithms
Opis:
The paper presents fragment of a larger study concerning the effective methods of solving the inverse boundary value problems. The boundary value problem described here is formulated as a problem of the identification of a boundary geometry with corner points. A method using a parametric integral equations system (PIES) is proposed. PIES used in the method makes the easy modelling of the geometry with corner points possible. This effect is obtained by the application of modified splines. An evolution algorithm is used for the effective control of modifications of the boundary geometry. Some experimental tests of the efficiency of the discussed method were performed for two-dimensional inverse potential problems.
Źródło:
TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk; 2002, 6, 4; 651-660
1428-6394
Pojawia się w:
TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The Asymptotical Stability of a Dynamic System With Structural Damping
Autorzy:
Hou, X.
Powiązania:
https://bibliotekanauki.pl/articles/908219.pdf
Data publikacji:
2003
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
matematyka
dynamic systems
evolution equation
asymptotic stability
Opis:
A dynamic system with structural damping described by partial differential equations is investigated. The system is first converted to an abstract evolution equation in an appropriate Hilbert space, and the spectral and semigroup properties of the system operator are discussed. Finally, the well-posedness and the asymptotical stability of the system are obtained by means of a semigroup of linear operators.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2003, 13, 2; 131-138
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Modeling ductile damage of steel in aggressive environment
Autorzy:
Kucharski, R.
Powiązania:
https://bibliotekanauki.pl/articles/1933197.pdf
Data publikacji:
2006
Wydawca:
Politechnika Gdańska
Tematy:
stress corrosion damage
reaction-diffusion equations
damage evolution equation
FEM
Opis:
This paper is a proposition of a new damage model, extended to include the influence of the external environment, based on the Gurson yield function and a new damage evolution equation. The model also contains a mass transport equation based on Pick's law. A comparison of experimental and numerical results is included.
Źródło:
TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk; 2006, 10, 4; 417-425
1428-6394
Pojawia się w:
TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Generalized method of Lie-algebraic discrete approximations for solving Cauchy problems with evolution equation
Autorzy:
Kindybaliuk, A.
Powiązania:
https://bibliotekanauki.pl/articles/122439.pdf
Data publikacji:
2014
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
generalized method of Lie-algebraic discrete approximations
dynamical systems
evolution equation
finite dimensional quasi representation
approximations
Lagrange’s polynomial
factorial convergence
układy dynamiczne
aproksymacje
wielomian Lagrange'a
Opis:
We consider solving the Cauchy problem with an abstract linear evolution equation by means of the Generalized Method of Lie-algebraic discrete approximations. Discretization of the equation is performed by all variables in equation and leads to a factorial rate of convergence if Lagrange interpolation is used for building quasi representation of differential operator. The rank of a finite dimensional operator and approximation properties have been determined. Error estimations and the factorial rate of convergence have been proved.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2014, 13, 2; 51-62
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Kolmogorov equation solution: multiple scattering expansion and photon statistics evolution modeling
Autorzy:
Guirao, M.
Leble, S.
Powiązania:
https://bibliotekanauki.pl/articles/1954433.pdf
Data publikacji:
2014
Wydawca:
Politechnika Gdańska
Tematy:
Kolmogorov equation
Fokker-Planck equation
multiple scattering expansion
photon statistics evolution
single scattering term
X-rays in beryl
Opis:
We consider a formulation of the Cauchy problem for the Kolmogorov equation which corresponds to a localized source of particles to be scattered by a medium with a given scattering amplitude density. The multiple scattering ampl itudes are introduced and the corresponding series solution of the equation is constructed. We investigate the integral representation for the first series terms, its estimations and values of the photon number of finite and point receivers. Application to the LIDAR problem and X-ray beam scattering for orthogonal and inclined to a layer is considered.
Źródło:
TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk; 2014, 18, 2; 187--203
1428-6394
Pojawia się w:
TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Solitary wave solution to the nonlinear evolution equation in cascaded quadratic media beyond the slowly varying envelope approximations
Autorzy:
Sarma, A K
Biswas, A.
Powiązania:
https://bibliotekanauki.pl/articles/174484.pdf
Data publikacji:
2014
Wydawca:
Politechnika Wrocławska. Oficyna Wydawnicza Politechniki Wrocławskiej
Tematy:
solitons
integrability
exact solution
cascaded quadratic media
Opis:
We report an exact bright and dark soliton solution to the nonlinear evolution equation derived by MOSES and WISE (Phys. Rev. Lett. 97, 2006, 073903) for cascaded quadratic media beyond the slowly varying envelope approximations. The integrability aspects of the model are addressed. The travelling wave hypothesis as well as the ansatz method are employed to obtain an exact 1-soliton solution. Both bright and dark soliton solutions are obtained. The corresponding constraint conditions are obtained in order for the soliton solutions to exist.
Źródło:
Optica Applicata; 2014, 44, 2; 205-212
0078-5466
1899-7015
Pojawia się w:
Optica Applicata
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Effect of capillarity on fourth order nonlinear evolution equation for two Stokes wave trains in deep water in the presence of air flowing over water
Autorzy:
Dhar, A. K.
Mondal, J.
Powiązania:
https://bibliotekanauki.pl/articles/265884.pdf
Data publikacji:
2015
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
nonlinear evolution equation
surface capillary gravity wave
stability
grawitacja
fala kapilarna
równania nieliniowe
Opis:
Fourth order nonlinear evolution equations, which are a good starting point for the study of nonlinear water waves, are derived for deep water surface capillary gravity waves in the presence of second waves in which air is blowing over water. Here it is assumed that the space variation of the amplitude takes place only in a direction along which the group velocity projection of the two waves overlap. A stability analysis is made for a uniform wave train in the presence of a second wave train. Graphs are plotted for the maximum growth rate of instability wave number at marginal stability and wave number separation of fastest growing sideband component against wave steepness. Significant improvements are noticed from the results obtained from the two coupled third order nonlinear Schrödinger equations.
Źródło:
International Journal of Applied Mechanics and Engineering; 2015, 20, 2; 267-282
1734-4492
2353-9003
Pojawia się w:
International Journal of Applied Mechanics and Engineering
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Fourth order nonlinear evolution equation for interfacial gravity waves in the presence of air flowing over water and a basic current shear
Autorzy:
Majumder, D. P.
Dhar, A. K.
Powiązania:
https://bibliotekanauki.pl/articles/265668.pdf
Data publikacji:
2015
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
nonlinear evolution equation
basic current shear
Stokes gravity wave
równania nieliniowe
przepływy Stokes'a
grawitacja
Opis:
A fourth order nonlinear evolution equation, which is a good starting point for the study of nonlinear water waves as first pointed out by Dysthe (1979) is derived for gravity waves propagating at the interface of two superposed fluids of infinite depth in the presence of air flowing over water and a basic current shear. A stability analysis is then made for a uniform Stokes gravity wave train. Graphs are plotted for the maximum growth rate of instability and for wave number at marginal stability against wave steepness for different values of air flow velocity and basic current shears. Significant deviations are noticed from the results obtained from the third order evolution equation, which is the nonlinear Schrödinger equation.
Źródło:
International Journal of Applied Mechanics and Engineering; 2015, 20, 3; 517-530
1734-4492
2353-9003
Pojawia się w:
International Journal of Applied Mechanics and Engineering
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Optimal control of general McKean-Vlasov stochastic evolution equations on Hilbert spaces and necessary conditions of optimality
Autorzy:
Ahmed, N.
Powiązania:
https://bibliotekanauki.pl/articles/729626.pdf
Data publikacji:
2015
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
McKean-Vlasov stochastic differential equation
Hilbert spaces
relaxed controls
existence of optimal controls
Opis:
In this paper we consider controlled McKean-Vlasov stochastic evolution equations on Hilbert spaces. We prove existence and uniqueness of solutions and regularity properties thereof. We use relaxed controls, adapted to a current of sub-sigma algebras generated by observable processes, and taking values from a Polish space. We introduce an appropriate topology based on weak star convergence. We prove continuous dependence of solutions on controls with respect to appropriate topologies. Theses results are then used to prove existence of optimal controls for Bolza problems. Then we develop the necessary conditions of optimality based on semi-martingale representation theory on Hilbert spaces. Next we show that the adjoint processes arising from the necessary conditions optimality can be constructed from the solution of certain BSDE.
Źródło:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2015, 35, 2; 165-195
1509-9407
Pojawia się w:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Problem with integral condition for evolution equation
Autorzy:
Kalenyuk, P. I.
Kuduk, G.
Kohut, I. V.
Nytrebych, Z. M.
Powiązania:
https://bibliotekanauki.pl/articles/357782.pdf
Data publikacji:
2015
Wydawca:
Politechnika Rzeszowska im. Ignacego Łukasiewicza. Oficyna Wydawnicza
Tematy:
analiza funkcjonalna
przestrzeń Banacha
równania ewolucyjne
równania różniczkowe
functional analysis
Banach space
evolution equation
integral conditions
differential-symbol method
Opis:
We propose a method of solving the problem with non-homogeneous integral condition for homogeneous evolution equation with abstract operator in a linear space H. For right-hand side of the integral condition which belongs to the special subspace H ⊆ L, in which the vectors are represented using Stieltjes integrals over a certain measure, the solution of the problem is represented in the form of Stieltjes integral over the same measure.
Źródło:
Journal of Mathematics and Applications; 2015, 38; 71-76
1733-6775
2300-9926
Pojawia się w:
Journal of Mathematics and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 26

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