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Wyświetlanie 1-15 z 77
Tytuł:
A Mesh-Independence Principle for Quadratic Penalties Applied to Semilinear Elliptic Boundary Control
Autorzy:
Grossman, Christian
Winkler, Max
Powiązania:
https://bibliotekanauki.pl/articles/1373554.pdf
Data publikacji:
2012
Wydawca:
Uniwersytet Jagielloński. Wydawnictwo Uniwersytetu Jagiellońskiego
Tematy:
optimal boundary control
mesh-independence principle
penalty methods for control constraints
weakly nonlinear elliptic equations
Opis:
The quadratic loss penalty is a well known technique for optimization and control problems to treat constraints. In the present paper they are applied to handle control bounds in a boundary control problems with semilinear elliptic state equations. Unlike in the case of finite dimensional optimization for infinite dimensional problems the order of convergence could only be roughly estimated, but numerical experiments revealed a clearly better convergence behavior with constants independent of the dimension of the used discretization. The main result in the present paper is the proof of sharp convergence bounds for both, the finite und infinite dimensional problem with a mesh-independence in case of the discretization. Further, to achieve an efficient realization of penalty methods the principle of control reduction is applied, i.e. the control variable is represented by the adjoint state variable by means of some nonlinear function. The resulting optimality system this way depends only on the state and adjoint state. This system is discretized by conforming linear finite elements. Numerical experiments show exactly the theoretically predicted behavior of the studied penalty technique.
Źródło:
Schedae Informaticae; 2012, 21; 9-26
0860-0295
2083-8476
Pojawia się w:
Schedae Informaticae
Dostawca treści:
Biblioteka Nauki
Artykuł
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:
A note on solutions of semilinear equations at resonance in a cone
Autorzy:
Przeradzki, Bogdan
Powiązania:
https://bibliotekanauki.pl/articles/1311896.pdf
Data publikacji:
1993
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
nonnegative solutions
equations at resonance
Opis:
A connection between the Landesman-Lazer condition and the solvability of the equation Lx = N(x) in a cone with a noninvertible linear operator L is studied. The result is based on the abstract framework from [5], applied to the existence of periodic solutions of ordinary differential equations, and compared with theorems by Santanilla (see [7]).
Źródło:
Annales Polonici Mathematici; 1993, 58, 1; 95-103
0066-2216
Pojawia się w:
Annales Polonici Mathematici
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:
An abstract semilinear first order differential equation in the hyperbolic case
Autorzy:
Bochenek, Jan
Powiązania:
https://bibliotekanauki.pl/articles/1311559.pdf
Data publikacji:
1995
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
semilinear initial value problem
stable family of operators
hyperbolic case
Opis:
This paper is devoted to the investigation of the abstract semilinear initial value problem $du/dt = A(t)u + f(t,u), u(0) = u_0$, in the "hyperbolic" case.
Źródło:
Annales Polonici Mathematici; 1995, 61, 1; 13-23
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
An existence result for impulsive functional differential inclusions in Banach spaces
Autorzy:
Benedetti, Irene
Powiązania:
https://bibliotekanauki.pl/articles/729505.pdf
Data publikacji:
2004
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
impulsive functional differential inclusion
semilinear differential inclusion
mild solution
Cauchy problem
solution set
condensing multimap
fixed point
Opis:
We use the topological degree theory for condensing multimaps to present an existence result for impulsive semilinear functional differential inclusions in Banach spaces. Moreover, under some additional assumptions we prove the compactness of the solution set.
Źródło:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2004, 24, 1; 13-30
1509-9407
Pojawia się w:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
An existence theorem for set differential inclusions in a semilinear metric space
Autorzy:
De Blasi, F. S.
Lakshmikantham, V.
Bhaskar, T. G.
Powiązania:
https://bibliotekanauki.pl/articles/970280.pdf
Data publikacji:
2007
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
approximate continuous selections
Cauchy problem
set differential inclusions
Hukuhara derivative
Opis:
Using the notion of continuous approximate selections, we establish an existence theorem for set differential inclusions in a semi-linear metric space.
Źródło:
Control and Cybernetics; 2007, 36, 3; 571-582
0324-8569
Pojawia się w:
Control and Cybernetics
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:
Approximate controllability for semilinear heat equations with globally Lipschitz nonlinearities
Autorzy:
Zuazua, E.
Powiązania:
https://bibliotekanauki.pl/articles/206681.pdf
Data publikacji:
1999
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
controllability
nolinear PDEs of parabolic type
systems governed by PDFs
Opis:
We consider the semilinear heat equation involving gradient terms in a bounded domain of [R^n]. It is assumed that the non-linearity is globally Lipschitz. We prove that the system is approximately controllable when t1e control acts on a bounded subset of the domain. The proof uses a variant of a classical fixed point method and is a simpler alternative to the earlier proof existing in the literature by means of the penalization of an optimal control problem. We also prove that the contool may be built so that, in addition to the approximate controllability requirement, it ensures that the state reaches exactly a finite number of constraints.
Źródło:
Control and Cybernetics; 1999, 28, 3; 665-683
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Approximate controllability of the impulsive semilinear heat equation
Autorzy:
Leiva, H.
Merentes, N.
Powiązania:
https://bibliotekanauki.pl/articles/357798.pdf
Data publikacji:
2015
Wydawca:
Politechnika Rzeszowska im. Ignacego Łukasiewicza. Oficyna Wydawnicza
Tematy:
impulsive semilinear heat equation
approximate controllability
Rothe's fixed point theorem
functional analysis
teoria punktu stałego
przestrzeń Banacha
równanie przewodnictwa ciepła
sterowalność
analiza funkcjonalna
Opis:
In this paper we apply Rothe's Fixed Point Theorem to prove the interior approximate controllability of the following semilinear impulsive Heat Equation \[ \begin{cases} z_{t} = \Delta z + 1_{\omega}u(t,x) + f(t,z,u(t,x)), & \text{in} \quad (0,\tau] \times \Omega, t \neq t_{k}) \\ z = 0, & \text{on} \quad (0, \tau) \times \delta\Omega,\\ z(0,x) = z_{0}(x), & x \in \Omega, \\ z(t_{k}^{+}, x) = z(t_{k}^{-}, x) + I_{k}(t_{k},z(t_{k},x)u(t_{k},x)), & x \in \Omega, \end{cases} \] where k = 1, 2, . . . , p, $\Omega$ is a bounded domain in $\mathbb{R}^{N}(N \geq 1), z_{0} \in L_{2}(\Omega), \omega$ is an open nonempty subset of $\Omega$, $1_{\omega}$ denotes the characteristic function of the set $\omega$, the distributed control $u$ belongs to $C\left([0, \tau]; L_{2}\left(\Omega\right)\right)$ and $f,I_{k} \in C([0, \tau] \times \mathbb{R} \times \mathbb{R}; \mathbb{R}), k = 1, 2, 3, \ldots, p$, such that \[ |f(t,z,u)| \leq a_{0}|z|^{\alpha_{0}} + b_{0}|u|^{\beta_{0}} +c_{0}, \quad u \in \mathbb{R}, z \in \mathbb{R}. \] \[ |I_{k}(t,z,u)| \leq a_{k}|z|^{\alpha_{k}} + b_{k}|u|^{\beta_{k}} +c_{k}, k=1,2,3 \ldots, pu \in \mathbb{R}, z \in \mathbb{R} \] with $\frac{1}{2} \leq \alpha_{k} < 1, \frac{1}{2} \leq \beta_{k} < 1, k= 0,1,2,3, \ldots, p$ Under this condition we prove the following statement: For all open nonempty subsets $\omega$ of $\Omega$ the system is approximately controllable on $[0, \tau]$. Moreover, we could exhibit a sequence of controls steering the nonlinear system from an initial state $z_{0}$ to an $\epsilon$ neighborhood of the nal state $z_{1}$ at time $\tau > 0$.
Źródło:
Journal of Mathematics and Applications; 2015, 38; 85-104
1733-6775
2300-9926
Pojawia się w:
Journal of Mathematics and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Approximate Controllability Properties of the Semilinear Heat Equation With Lumped Controls
Autorzy:
Khapalov, A. Y.
Powiązania:
https://bibliotekanauki.pl/articles/908269.pdf
Data publikacji:
1999
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
sterowność
sterowanie skupione
semilinear heat equation
controllability
internal lumped control
Opis:
In this article, we study the global controllability properties of aone-dimensional semilinear heat equation with sublinear reaction term, governed in a bounded domain by internal lumped controls. We prove thatit is possible to exactly control any finite dimensional portion of its solution (when expanded along the sequence of the eigenfunctions of the associated Laplacian), provided that the truncated linear equationis approximately controllable in L^2 (0,1). We also describe a certain topology (weaker than L^2 (0,1)) in which this system is, in fact, globally approximately controllable at any positive time. Some extensions to the case of several dimensions are also given.
Źródło:
International Journal of Applied Mathematics and Computer Science; 1999, 9, 4; 751-765
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Asymptotic behavior of positive solutions of a semilinear Dirichlet problem in the annulus
Autorzy:
Dridi, S.
Khamessi, B.
Powiązania:
https://bibliotekanauki.pl/articles/254947.pdf
Data publikacji:
2015
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
asymptotic behavior
Dirichlet problem
Karamata function
subsolution
supersolution
Opis:
In this paper, we establish existence and asymptotic behavior of a positive classical solution to the following semilinear boundary value problem: [formula] Here O is an annulus in [formula] and q is a positive function in [formula], satisfying some appropriate assumptions related to Karamata regular variation theory. Our arguments combine a method of sub- and supersolutions with Karamata regular variation theory.
Źródło:
Opuscula Mathematica; 2015, 35, 1; 21-36
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
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:
Banach fixed-point theorem in semilinear controllability problems – a survey
Autorzy:
Klamka, J.
Babiarz, A.
Niezabitowski, M.
Powiązania:
https://bibliotekanauki.pl/articles/200909.pdf
Data publikacji:
2016
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
complete controllability
Banach space
Hilbert space
fixed-point
infinite dimensional space
sterowność
przestrzeń Banacha
przestrzeń Hilberta
Opis:
The main aim of this article is to review the existing state of art concerning the complete controllability of semilinear dynamical systems. The study focus on obtaining the sufficient conditions for the complete controllability for various systems using the Banach fixedpoint theorem. We describe the results for stochastic semilinear functional integro-differential system, stochastic partial differential equations with finite delays, semilinear functional equations, a stochastic semilinear system, a impulsive stochastic integro-differential system, semilinear stochastic impulsive systems, an impulsive neutral functional evolution integro-differential system and a nonlinear stochastic neutral impulsive system. Finally, two examples are presented.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2016, 64, 1; 21-35
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 77

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