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Wyświetlanie 1-15 z 41
Tytuł:
A new composition theorem for sp-weighted pseudo almost periodic functions and applications to semilinear differential equations
Autorzy:
Zhao, Z.
Chang, Y.
N'Guerekata, G. M.
Powiązania:
https://bibliotekanauki.pl/articles/256044.pdf
Data publikacji:
2011
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
Sp-weighted pseudo almost periodic
weighted pseudo almost periodicity
semilinear differential equations
Opis:
In this paper, we establish a new composition theorem for Sp-weighted pseudo almost periodic functions under weaker conditions than the Lipschitz ones currently encountered in the literatures. We apply this new composition theorem along with the Schauder's fixed point theorem to obtain new existence theorems for weighted pseudo almost periodic mild solutions to a semilinear differential equation in a Banach space.
Źródło:
Opuscula Mathematica; 2011, 31, 3; 457-474
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
An output controllability problem for semilinear distributed hyperbolic systems
Autorzy:
Zerrik, E.
Larhrissi, R.
Bourray, H.
Powiązania:
https://bibliotekanauki.pl/articles/929815.pdf
Data publikacji:
2007
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
system o parametrach rozłożonych
system półliniowy
system hyperboliczny
sterowność wymuszona
punkt stały
distributed-parameter systems
semilinear hyperbolic systems
constrained controllability
fixed point
Opis:
The paper aims at extending the notion of regional controllability developed for linear systems to the semilinear hyperbolic case. We begin with an asymptotically linear system and the approach is based on an extension of the Hilbert uniqueness method and Schauder’s fixed point theorem. The analytical case is then tackled using generalized inverse techniques and converted to a fixed point problem leading to an algorithm which is successfully implemented numerically and illustrated with examples.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2007, 17, 4; 437-446
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
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:
Convergence of Tolands critical points for sequences of D.C. functions and application to the resolution of semilinear elliptic problems
Autorzy:
Yassine, A.
Alaa, N.
Elhilali Alaoui, A.
Powiązania:
https://bibliotekanauki.pl/articles/206580.pdf
Data publikacji:
2001
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
algorytm proksymalny
funkcje D.C.
optymalizacja niewypukła
punkt krytyczny Tolanda
semiliniowe zagadnienie eliptyczne
dc functions
non-convex optimization
normalized D.C. decomposition
proximal algorithm
semilinear elliptic problem
Toland's critical point
Opis:
We prove that if a sequence (fn)n of D.C. functions (Difference of two Convex functions) converges to a D.C. function f in some appropriate way and if un is a critical point of fn, in the sense described by Toland, and is such that (un)n converges to u, then a is a critical point of f, still in Toland's sense. We also build a new algorithm which searches for this critical point u and then apply it in order to compute the solution of a semilinear elliptic equation.
Źródło:
Control and Cybernetics; 2001, 30, 4; 405-417
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the constrained and unconstrained controllability of semilinear Hilfer fractional systems
Autorzy:
Sikora, Beata
Powiązania:
https://bibliotekanauki.pl/articles/27312002.pdf
Data publikacji:
2023
Wydawca:
Polska Akademia Nauk. Czasopisma i Monografie PAN
Tematy:
Hilfer fractional derivative
fractional systems
semilinear control systems
nonautonomous systems
Rothe's fixed point theorem
generalized Darbo fixed point theorem
Opis:
In the paper finite-dimensional semilinear dynamical control systems described by fractional-order state equations with the Hilfer fractional derivative are discussed. The formula for a solution of the considered systems is presented and derived using the Laplace transform. Bounded nonlinear function f depending on a state and controls is used. New sufficient conditions for controllability without constraints are formulated and proved using Rothe’s fixed point theorem and the generalized Darbo fixed point theorem. Moreover, the stability property is used to formulate constrained controllability criteria. An illustrative example is presented to give the reader an idea of the theoretical results obtained. A transient process in an electrical circuit described by a system of Hilfer type fractional differential equations is proposed as a possible application of the study.
Źródło:
Archives of Control Sciences; 2023, 33, 1; 155--178
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Existence and controllability results for semilinear neutral functional differential inclusions with nonlocal conditions
Autorzy:
Ntouyas, S.
O'Regan, D.
Powiązania:
https://bibliotekanauki.pl/articles/729421.pdf
Data publikacji:
2007
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
semilinear differential inclusions
nonlocal conditions
analytic semigroups
cosine functions
integrated semigroups
fixed point
nonlinear alternative
controllability
Opis:
In this paper, we prove existence and controllability results for first and second order semilinear neutral functional differential inclusions with finite or infinite delay in Banach spaces, with nonlocal conditions. Our theory makes use of analytic semigroups and fractional powers of closed operators, integrated semigroups and cosine families.
Źródło:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2007, 27, 2; 213-264
1509-9407
Pojawia się w:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On convergence of regularization methods for nonlinear parabolic optimal control problems with control and state constraints
Autorzy:
Neitzel, I.
Troltzsch, F.
Powiązania:
https://bibliotekanauki.pl/articles/970314.pdf
Data publikacji:
2008
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
optimal control
semilinear parabolic equation
pointwise state constraints
Moreau-Yosida regularization
Lavrentiev regularization
convergence
strong regularity
local uniqueness
Opis:
Moreau-Yosida and Lavrentiev type regularization methods are considered for nonlinear optimal control problems governed by semilinear parabolic equations with bilateral pointwise control and state constraints. The convergence of optimal controls of the regularized problems is studied for regularization parameters tending to infinity or zero, respectively. In particular, the strong convergence of global and local solutions is addressed. Moreover, strong regularity of the Lavrentiev-regularized optimality system is shown under certain assumptions, which, in particular, allows to show that locally optimal solutions of the Lavrentiev regularized problems are locally unique. This analysis is based on a second-order sufficient optimality condition and a separation assumption on almost active sets.
Źródło:
Control and Cybernetics; 2008, 37, 4; 1013-1043
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Existence and decay of finite energy solutions for semilinear dissipative wave equations in time-dependent domains
Autorzy:
Nakao, Mitsuhiro
Powiązania:
https://bibliotekanauki.pl/articles/1397374.pdf
Data publikacji:
2021
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
energy decay
global existence
semilinear wave equation
noncylindrical domains
Opis:
We consider the initial-boundary value problem for semilinear dissipative wave equations in noncylindrical domain $\cup_{0 \leq t \leq \infty} \Omega(t) \times \{t\} \subset \mathbb{R}^N \times \mathbb{R}$. We are interested in finite energy solution. We derive an exponential decay of the energy in the case Ω(t) is bounded in $\mathbb{R}^N$ and the estimate $\int_0^\infty E(t)dt \leq C(E(0), ||u(0)||) < \infty $ in the case Ω (t) is unbounded. Existence and uniqueness of finite energy solution are also proved.
Źródło:
Opuscula Mathematica; 2020, 40, 6; 725-736
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Optimal control of semilinear evolution inclusions via discrete approximations
Autorzy:
Mordukhovich, B. S.
Wang, D.
Powiązania:
https://bibliotekanauki.pl/articles/1839178.pdf
Data publikacji:
2005
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
sterowanie optymalne
analiza wariacyjna
różniczkowanie uogólnione
aproksymacja dyskretna
warunek konieczny optymalności
optimal control
variational analysis
generalized differentiation
semilinear evolution inclusions
discrete approximations
necessary optimality conditions
Opis:
This paper studies a Mayer type optimal control problem with general endpoint constraints for semilinear unbounded evolution inclusions in reflexive and separable Banach spaces. First, we construct a sequence of discrete approximations to the original optimal control problem for evolution inclusions and prove that optimal solutions to discrete approximation problems uniformly converge to a given optimal solution for the original continuous-time problem. Then, based on advanced tools of generalized differentiation, we derive necessary optimality conditions for discrete-time problems under fairly general assumptions. Combining these results with recent achievements of variational analysis in infinite-dimensional spaces, we establish new necessary optimality conditions for constrained continuous-time evolution inclusions by passing to the limit from discrete approximations.
Źródło:
Control and Cybernetics; 2005, 34, 3; 849-870
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Asymptotic Properties of Stochastic Semilinear Equations by the Method of Lower Measures
Autorzy:
Maslowski, B.
Simão, I.
Powiązania:
https://bibliotekanauki.pl/articles/966652.pdf
Data publikacji:
1997
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
invariant measures
mixing
stochastic semilinear equations
ergodicity
Źródło:
Colloquium Mathematicum; 1997, 72, 1; 147-171
0010-1354
Pojawia się w:
Colloquium Mathematicum
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Existence theorems for a semilinear elliptic boundary value problem
Autorzy:
Marano, Salvatore
Powiązania:
https://bibliotekanauki.pl/articles/1311657.pdf
Data publikacji:
1994
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
elliptic differential inclusions
semilinear elliptic equations
strong solutions
Opis:
Let Ω be a bounded domain in $ℝ^n$, n ≥ 3, with a smooth boundary ∂Ω; let L be a linear, second order, elliptic operator; let f and g be two real-valued functions defined on Ω × ℝ such that f(x,z) ≤ g(x,z) for almost every x ∈ Ω and every z ∈ ℝ. In this paper we prove that, under suitable assumptions, the problem { f(x,u) ≤ Lu ≤ g(x,u)   in Ω, u = 0     on ∂Ω, has at least one strong solution $u ∈ W^{2,p}(Ω) ∩ W^{1,p}_0(Ω). Next, we present some remarkable special cases.
Źródło:
Annales Polonici Mathematici; 1994-1995, 60, 1; 57-67
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Input reconstruction by feedback control for the Schlögl and FitzHugh–Nagumo equations
Autorzy:
Maksimov, Vyacheslav
Trlötzsch, Fredi
Powiązania:
https://bibliotekanauki.pl/articles/329903.pdf
Data publikacji:
2020
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
semilinear parabolic equation
input reconstruction
feedback control
równanie paraboliczne
równanie semiliniowe
sprzężenie zwrotne
Opis:
Dynamical reconstruction of unknown time-varying controls from inexact measurements of the state function is investigated for a semilinear parabolic equation with memory. This system includes as particular cases the Schlögl model and the FitzHugh–Nagumo equations. A numerical method is suggested that is based on techniques of feedback control. An error analysis is performed. Numerical examples confirm the theoretical predictions.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2020, 30, 1; 5-22
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A viability result for nonconvex semilinear functional differential inclusions
Autorzy:
Lupulescu, Vasile
Necula, Mihai
Powiązania:
https://bibliotekanauki.pl/articles/729593.pdf
Data publikacji:
2005
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
viability
invariance
tangency condition
semilinear differential inclusions
Opis:
We establish some sufficient conditions in order that a given locally closed subset of a separable Banach space be a viable domain for a semilinear functional differential inclusion, using a tangency condition involving a semigroup generated by a linear operator.
Źródło:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2005, 25, 1; 109-128
1509-9407
Pojawia się w:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On periodic oscillations for a class of feedback control systems in Hilbert spaces
Autorzy:
Loi, Nguyen
Powiązania:
https://bibliotekanauki.pl/articles/729532.pdf
Data publikacji:
2013
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
semilinear differential inclusion
periodic solution
guiding function
Opis:
In this paper, by using the topological degree theory for multivalued maps and the method of guiding functions in Hilbert spaces we deal with the existence of periodic oscillations for a class of feedback control systems in Hilbert spaces.
Źródło:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2013, 33, 2; 205-219
1509-9407
Pojawia się w:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Nonoverlapping domain decomposition for optimal control problems governed by semilinear models for gas flow in networks
Autorzy:
Leugering, G.
Martin, A.
Schmidt, M.
Sirvent, M.
Powiązania:
https://bibliotekanauki.pl/articles/205527.pdf
Data publikacji:
2017
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
optimal control
gas networks
Euler equation
semilinear PDE
nonoverlapping domain decomposition
Opis:
We consider optimal control problems for gas flow in pipeline networks. The equations of motion are taken to be represented by a first-order system of hyperbolic semilinear equations derived from the fully nonlinear isothermal Euler gas equations. We formulate an optimal control problem on a network and introduce a tailored time discretization thereof. In order to further reduce the complexity, we consider an instantaneous control strategy. The main part of the paper is concerned with a nonoverlapping domain decomposition of the optimal control problem on the graph into local problems on smaller sub-graphs—ultimately on single edges. We prove convergence of the domain decomposition method on networks and study the wellposedness of the corresponding time-discrete optimal control problems. The point of the paper is that we establish virtual control problems on the decomposed subgraphs such that the corresponding optimality systems are in fact equal to the systems obtained via the domain decomposition of the entire optimality system.
Źródło:
Control and Cybernetics; 2017, 46, 3; 191-225
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 41

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