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Wyświetlanie 1-15 z 23
Tytuł:
Traveling waves in media with diffusion
Autorzy:
Kaźmierczak, Bogdan
Powiązania:
https://bibliotekanauki.pl/articles/747755.pdf
Data publikacji:
2005
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
Reaction-diffusion equations, Boundary value problems for parabolic systems,Index theory, Morse-Conley indices, Homoclinic and heteroclinic orbits, Ionized gas flow in electromagnetic fields
plasmic flow, Physiological flow
Opis:
In this paper, we discuss traveling wave solutions for equations that model nonlinear media with diffusion. Such solutions can also describe, for example, the propagation of heteroclinic fronts or impulses (medium excitations). We present several examples of processes in which the notion of a traveling wave captures the essence of the analytical phenomena, including plasma sustained by a laser beam, phase transitions in van der Waals fluids, skin morphogenesis, and the DNA-RNA transcription process.
Źródło:
Mathematica Applicanda; 2005, 33, 47/06
1730-2668
2299-4009
Pojawia się w:
Mathematica Applicanda
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Study of ODE limit problems for reaction-diffusion equations
Autorzy:
Simsen, J.
Simsen, M. S.
Zimmermann, A.
Powiązania:
https://bibliotekanauki.pl/articles/1397881.pdf
Data publikacji:
2018
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
ODE limit problems
shadow systems
reaction-diffusion equations
parabolic problems
variable exponents
attractors
upper semicontinuity
Opis:
In this work we study ODE limit problems for reaction-diffusion equations for large diffusion and we study the sensitivity of nonlinear ODEs with respect to initial conditions and exponent parameters. Moreover, we prove continuity of the flow and weak upper semicontinuity of a family of global attractors for reaction-diffusion equations with spatially variable exponents when the exponents go to 2 in $L^\infty(\Omega)$ and the diffusion coefficients go to infinity.
Źródło:
Opuscula Mathematica; 2018, 38, 1; 117-131
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Stability of solutions of infinite systems of nonlinear differential-functional equations of parabolic type
Autorzy:
Zabawa, T.S.
Powiązania:
https://bibliotekanauki.pl/articles/254967.pdf
Data publikacji:
2006
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
stability of solutions
infinite systems
parabolic equations
elliptic equations
semilinear differential-functional equations
monotone iteration method
Opis:
A parabolic initial boundary value problem and an associated elliptic Dirichlet problem for an infinite weakly coupled system of semilinear differential-functional equations are considered. It is shown that the solutions of the parabolic problem is asymptotically stable and the limit of the solution of the parabolic problem as t → ∞ is the solution of the associated elliptic problem. The result is based on the monotone methods.
Źródło:
Opuscula Mathematica; 2006, 26, 1; 173-183
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Solving Parabolic Equations by Using the Method of Fast Convergent Iterations
Autorzy:
Bondarenko, V.
Bidyuk, P.
Bernatska, J.
Powiązania:
https://bibliotekanauki.pl/articles/911186.pdf
Data publikacji:
2000
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
fundamental solution
Riemannian manifold
rate of convergence
iteration technique
numerical simulation
parabolic equations
równanie paraboliczne
rozwiązanie podstawowe
symulacja numeryczna
Opis:
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.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2000, 10, 2; 333-344
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Planowanie eksperymentu dla wyznaczania warunku początkowego układu o parametrach rozłożonych
Design of experiments for initial conditions identification in distributed - parameter systems
Autorzy:
Szewczyk, D.
Powiązania:
https://bibliotekanauki.pl/articles/153512.pdf
Data publikacji:
2007
Wydawca:
Stowarzyszenie Inżynierów i Techników Mechaników Polskich
Tematy:
układy o parametrach rozłożonych
rozmieszczenie czujników
estymacja parametrów
równanie różniczkowe cząstkowe
obserwowalność
distributed parameter systems
sensor location
linear parabolic equations
observability
Opis:
W pracy przedstawiony został problem optymalnego rozmieszczenia czujników pomiarowych dla liniowego układu o parametrach rozłożonych opisanego równaniem różniczkowym cząstkowym typu parabolicznego z mieszanymi warunkami brzegowymi. Przedstawiony jest również sposób wyznaczenia przybliżenia funkcyjnego warunku początkowego.
The optimum experimental design problem for linear distributed parameter systems described by linear parabolic equations is considered. The approach, based on appropriate optimization techniques, shows how to construct and determine the initial state.
Źródło:
Pomiary Automatyka Kontrola; 2007, R. 53, nr 10, 10; 7-11
0032-4140
Pojawia się w:
Pomiary Automatyka Kontrola
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On an optimal control problem for a quasilinear parabolic equation
Autorzy:
Farag, S.
Farag, M.
Powiązania:
https://bibliotekanauki.pl/articles/1208213.pdf
Data publikacji:
2000
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
existence theory
parabolic equations
penalty function methods
optimal control
Opis:
An optimal control problem governed by a quasilinear parabolic equation with additional constraints is investigated. The optimal control problem is converted to an optimization problem which is solved using a penalty function technique. The existence and uniqueness theorems are investigated. The derivation of formulae for the gradient of the modified function is explainedby solving the adjoint problem.
Źródło:
Applicationes Mathematicae; 2000, 27, 2; 239-250
1233-7234
Pojawia się w:
Applicationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Nonlocal quadratic evolution problems
Autorzy:
Biler, Piotr
Woyczyński, Wojbor
Powiązania:
https://bibliotekanauki.pl/articles/1207633.pdf
Data publikacji:
2000
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
self-similar solutions
fractal anomalous diffusion
asymptotic behavior of solutions
nonlinear nonlocal parabolic equations
Opis:
Nonlinear nonlocal parabolic equations modeling the evolution of density of mutually interacting particles are considered. The inertial type nonlinearity is quadratic and nonlocal while the diffusive term, also nonlocal, is anomalous and fractal, i.e., represented by a fractional power of the Laplacian. Conditions for global in time existence versus finite time blow-up are studied. Self-similar solutions are constructed for certain homogeneous initial data. Monte Carlo approximation schemes by interacting particle systems are also mentioned.
Źródło:
Banach Center Publications; 2000, 52, 1; 11-24
0137-6934
Pojawia się w:
Banach Center Publications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Monotone iterative methods for infinite systems of reaction-diffusion-convection equations with functional dependence
Autorzy:
Brzychczy, S.
Powiązania:
https://bibliotekanauki.pl/articles/255097.pdf
Data publikacji:
2005
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
infinite systems
reaction-diffusion-convection equations
semilinear parabolic differential-functional equations
Volterra functionals
monotone iterative methods
method of upper and lower solutions
Opis:
We consider the Fourier first initial-boundary value problem for an infinite system of semilinear parabolic differential-functional equations of reaction-diffusion-convection type of the form [formula] where [formula] in a bounded cylindrical domain (0, T] x G := D rcup Rm+1. The right-hand sides of the system are Volterra type functionals of the unknown function z. In the paper, we give methods of the construction of the monotone iterative sequences converging to the unique classical solution of the problem considered in partially ordered Banach spaces with various convergence rates of iterations. We also give remarks on monotone iterative methods in connection with numerical methods, remarks on methods for the construction of lower and upper solutions and remarks concerning the possibility of extending these methods to more general parabolic equations. All monotone iterative methods are based on differential inequalities and, in this paper, we use the theorem on weak partial differential-functional inequalities for infinite systems of parabolic equations, the comparison theorem and the maximum principle. A part of the paper is based on the results of our previous papers. These results generalize the results obtained by several authors in numerous papers for finite systems of semilinear parabolic differential equations to encompass the case of infinite systems of semilinear parabolic differential-functional equations. The monotone iterative schemes can be used for the computation of numerical solutions.
Źródło:
Opuscula Mathematica; 2005, 25, 1; 29-99
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Monotone iteration for infinite systems of parabolic equations
Autorzy:
Pudełko, A.
Powiązania:
https://bibliotekanauki.pl/articles/255193.pdf
Data publikacji:
2005
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
infinite systems
parabolic equations
Cauchy problem
monotone iteration method
differentail inequality
Opis:
In the paper the Cauchy problem for and infinite system of parabolic type equations is studied. The general operators of the parabolic type of second order with variable coefficients are considered and the system is weakly coupled. Among the obtained results there is a theorem on differential inequality as well as the existence and uniqueness theorem in the class of continuous-bounded functions obtained by monotone iterative method.
Źródło:
Opuscula Mathematica; 2005, 25, 2; 307-318
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Initial-boundary value problems for impulsive parabolic functional differential equations
Autorzy:
Bainov, D.
Kamont, Zdzisław
Minchev, E.
Powiązania:
https://bibliotekanauki.pl/articles/1339288.pdf
Data publikacji:
1996
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
initial-boundary value problems
impulsive parabolic equations
Opis:
Theorems on differential inequalities generated by an initial-boundary value problem for impulsive parabolic functional differential equations are considered. Comparison results implying uniqueness criteria are proved.
Źródło:
Applicationes Mathematicae; 1996-1997, 24, 1; 1-15
1233-7234
Pojawia się w:
Applicationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Global solutions via partial information and the Cahn-Hilliard equation
Autorzy:
Cholewa, Jan
Dłotko, Tomasz
Powiązania:
https://bibliotekanauki.pl/articles/1359015.pdf
Data publikacji:
1996
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
a priori estimates
Cahn-Hilliard equation
global existence
compact semigroups
higher order parabolic equations
Opis:
Global solutions of semilinear parabolic equations are studied in the case when some weak a priori estimate for solutions of the problem under consideration is already known. The focus is on the rapid growth of the nonlinear term for which existence of the semigroup and certain dynamic properties of the considered system can be justified. Examples including the famous Cahn-Hilliard equation are finally discussed.
Źródło:
Banach Center Publications; 1996, 33, 1; 39-50
0137-6934
Pojawia się w:
Banach Center Publications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Existence of solutions and monotone iterative method for infinite systems of parabolic differential-functional equations
Autorzy:
Brzychczy, Stanisław
Powiązania:
https://bibliotekanauki.pl/articles/1293995.pdf
Data publikacji:
1999
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
method of lower and upper functions
infinite systems of parabolic differential-functional equations
monotone iterative method
Opis:
We consider the Fourier first boundary value problem for an infinite system of weakly coupled nonlinear differential-functional equations. To prove the existence and uniqueness of solution, we apply a monotone iterative method using J. Szarski's results on differential-functional inequalities and a comparison theorem for infinite systems.
Źródło:
Annales Polonici Mathematici; 1999, 72, 1; 15-24
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Estimates of solutions for parabolic differential and difference functional equations and applications
Autorzy:
Sapa, L.
Powiązania:
https://bibliotekanauki.pl/articles/254895.pdf
Data publikacji:
2012
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
parabolic differential and discrete functional equations
estimate of solution
implicit difference method
Opis:
The theorems on the estimates of solutions for nonlinear second-order partial differential functional equations of parabolic type with Dirichlet's condition and for suitable implicit finite difference functional schemes are proved. The proofs are based on the comparison technique. The convergent and stable difference method is considered without the assumption of the global generalized Perron condition posed on the functional variable but with the local one only. It is a consequence of our estimates theorems. In particular, these results cover quasi-linear equations. However, such equations are also treated separately. The functional dependence is of the Volterra type.
Źródło:
Opuscula Mathematica; 2012, 32, 3; 529-549
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Distributed optimal control problems driven by space-time fractional parabolic equations
Autorzy:
Mehandiratta, Vaibhav
Mehra, Mani
Leugering, Günter
Powiązania:
https://bibliotekanauki.pl/articles/2183495.pdf
Data publikacji:
2022
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
space-time fractional parabolic equations
Caputo fractional derivative
distributed control
L1 method
Grünwald-Letnikov formula
Opis:
We study distributed optimal control problems, governed by space-time fractional parabolic equations (STFPEs) involving time-fractional Caputo derivatives and spatial fractional derivatives of Sturm-Liouville type. We first prove existence and uniqueness of solutions of STFPEs on an open bounded interval and study their regularity. Then we show existence and uniqueness of solutions to a quadratic distributed optimal control problem. We derive an adjoint problem using the right-Caputo derivative in time and provide optimality conditions for the control problem. Moreover, we propose a finite difference scheme to find the approximate solution of the considered optimal control problem. In the proposed scheme, the well-known L1 method has been used to approximate the time-fractional Caputo derivative, while the spatial derivative is approximated using the Grünwald-Letnikov formula. Finally, we demonstrate the accuracy and the performance of the proposed difference scheme via examples.
Źródło:
Control and Cybernetics; 2022, 51, 2; 191--226
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Discrete relaxed method for semilinear parabolic optimal control problem
Autorzy:
Chryssoverghi, I.
Coletsos, J.
Kokkinis, B.
Powiązania:
https://bibliotekanauki.pl/articles/205973.pdf
Data publikacji:
1999
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
sterowanie optymalne
accumulation points
discrete optimisation method
discretization
distributed control
minimum principle
optimal control
parabolic equations
partial differential equations
penalty method
relaxed control
semilinear parabolic system
Opis:
We consider an optimal control problem for systems governed by semilinear parabolic partial differential equations with control and state constraints, without any convexity assumptions. A discrete optimization method is proposed to solve this problem in its relaxed form which combines a penalized Armijo type method with a finite element discretization and constructs sequences of discrete Gamkrelidze relaxed controls. Under appropriate assumptions, we prove that accumulation points of these sequences satisfy the relaxed Pontryagin necessary conditions for optimality. Moreover, we show that the Gamkrelidze controls thus generated can be replaced by simulating piecewise constant classical controls.
Źródło:
Control and Cybernetics; 1999, 28, 2; 157-176
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 23

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