PL
 |
EN
Preferencje help
Polish version English version Język
Widoczny [Schowaj] Abstrakt
Liczba wyników

Znaleziono wyników: 11

Liczba wyników na stronie
first rewind previous Strona / 1 next fast forward last
Wyniki wyszukiwania
Wyszukiwano:
w słowach kluczowych:  Green’s function
help Sortuj według:

help Ogranicz wyniki do:
first rewind previous Strona / 1 next fast forward last
1
Content available Green's functions and existence of solutions of nonlinear fractional implicit difference equations with Dirichlet boundary conditions
Cabada Alberto, Dimitrov Nikolay D., Jonnalagadda Jagan Mohan
Opuscula Mathematica
|
2024
|
Vol. 44, no. 2
167--195
EN
This article is devoted to deduce the expression of the Green’s function related to a general constant coefficients fractional difference equation coupled to Dirichlet conditions. In this case, due to the points where some of the fractional operators are applied, we are in presence of an implicit fractional difference equation. So, due to such a property, it is more complicated to calculate and manage the expression of the Green’s function than in the explicit case studied in a previous work of the authors. Contrary to the explicit case, where it is shown that the Green’s function is constructed as finite sums, the Green’s function constructed here is an infinite series. This fact makes necessary to impose more restrictive assumptions on the parameters that appear in the equation. The expression of the Green’s function will be deduced from the Laplace transform on the time scales of the integers. We point out that, despite the implicit character of the considered equation, we can have an explicit expression of the solution by means of the expression of the Green’s function. These two facts are not incompatible. Even more, this method allows us to have an explicit expression of the solution of an implicit problem. Finally, we prove two existence results for nonlinear problems, via suitable fixed point theorems.
2
Content available On the blowing up solutions of the 4-d general q-Kuramoto-Sivashinsky equation with exponentially “dominated” nonlinearity and singular weight
Baraket Sami, Mahdaoui Safia, Ouni Taieb
Opuscula Mathematica
|
2023
|
Vol. 43, no. 1
5--18
EN
Let Ω be a bounded domain in R4 with smooth boundary and let x1, x2, . . . , xm be m-points in Ω. We are concerned with the problem [formula], where the principal term is the bi-Laplacian operator, H(x, u, Dku) is a functional which grows with respect to Du at most like |Du|q, 1 ≤ q ≤ 4, f : Ω → [0,+∞[ is a smooth function satisfying f(pi) > 0 for any i = 1, . . . , n, αi are positives numbers and g : R → [0,+∞[ satisfy |g(u)| ≤ ceu. In this paper, we give sufficient conditions for existence of a family of positive weak solutions (uρ) ρ>0 in Ω under Navier boundary conditions u = Δu = 0 on ∂Ω. The solutions we constructed are singular as the parameters ρ tends to 0, when the set of concentration S = {x1, . . . , xm} ⊂ Ω and the set Λ := {p1, . . . , pn} ⊂ Ω are not necessarily disjoint. The proof is mainly based on nonlinear domain decomposition method.
3
Content available remote Positive solutions for fractional differential equation at resonance under integral boundary conditions
Wang Youyu, Huang Yue, Li Xianfei
Demonstratio Mathematica
|
2022
|
Vol. 55, nr 1
238--253
EN
By using the theory of fixed point index and spectral theory of linear operators, we study the existence of positive solutions for Riemann-Liouville fractional differential equations at resonance. Our approach will provide some new ideas for the study of this kind of problem.
4
Content available Region of existence of multiple solutions for a class of robin type four-point bvps
Verma Amit K., Urus Nazia, Agarwal Ravi P.
Opuscula Mathematica
|
2021
|
Vol. 41, no. 4
571--600
EN
This article aims to prove the existence of a solution and compute the region of existence for a class of four-point nonlinear boundary value problems (NLBVPs) defined as [formula] where I = [0, 1], 0 < ξ≥ η < 1 and λ 1 ,λ > 0. The nonlinear source term [formula] is one sided Lipschitz in u’ with Lipschitz constant L 1 and Lipschitz in u', such that [formula]. We develop monotone iterative technique (MI-technique) in both well ordered and reverse ordered cases. We prove maximum, anti-maximum principle under certain assumptions and use it to show the monotonic behaviour of the sequences of upper-lower solutions. The sufficient conditions are derived for the existence of solution and verified for two examples. The above NLBVPs is linearised using Newton’s quasilinearization method which involves a parameter k equivalent to max [formula]. We compute the range of k for which iterative sequences are convergent.
5
Content available remote A new iteration method for the solution of third-order BVP via Green's function
Akgun Fatma Aydın, Rasulov Zaur
Demonstratio Mathematica
|
2021
|
Vol. 54, nr 1
425--435
EN
In this study, a new iterative method for third-order boundary value problems based on embedding Green’s function is introduced. The existence and uniqueness theorems are established, and necessary conditions are derived for convergence. The accuracy, efficiency and applicability of the results are demonstrated by comparing with the exact results and existing methods. The results of this paper extend and generalize the corresponding results in the literature.
6
Content available remote Temperature-time profiles of a tubular bus in shorting conditions
Gołębiowski Jerzy, Zaręba Marek
Przegląd Elektrotechniczny
|
2020
|
R. 96, nr 3
146--149
EN
In the paper temperature-time profiles generated in a tubular bus under short-circuit conditions were determined. The initial-boundary parabolic problem was the mathematical model. Adiabatic boundaries of the system and field uniformity at the initial moment of shorting were assumed and motivated. The two models of the bus-bar electric resistivity were considered: the temperature dependent (variable) and averaged one (constant). The problem was solved by means of Green’s function. The one-second shorting current and its multi-second equivalents were determined based on the above. The analytical results were verified numerically by the finite element method.
PL
W artykule wyznaczono czasowe przebiegi temperatury generowane w szynoprzewodzie rurowym podczas zwarcia. Matematycznym modelem jest początkowo-brzegowe zagadnienie paraboliczne. Przyjęto i uzasadniono założenie o adiabatycznych brzegach układu oraz o równomierności pola w początkowej chwili zwarcia. Rozpatrywano dwa modele elektrycznej rezystywności szynoprzewodu: uzależnionej termicznie (zmiennej) i uśrednionej (stałej). Zagadnienie rozwiązano za pomocą funkcji Greena. Na tej podstawie wyznaczono jednosekundowy prąd zwarcia i jego wielosekundowe równoważniki. Wyniki analityczne zweryfikowano numerycznie metodą elementu skończonego.
7
Content available Matrix Green's function of double-diffusivity problem and its applications to problems with inner point source
Chaplya Yevhen, Chernukha Olha, Bilushchak Yurii
TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk
|
2019
|
Vol. 23, No 1
75--99
EN
The matrix Green’s function of the initial-boundary value problem of admixture double-diffusivity is defined. The initial-boundary value problem with a point source is formulated for the matrix elements for determination of the matrix Green’s function. Formulae for matrix elements are obtained and the behavior of Green’s functions is investigated. It is shown that the surface generated by the Green’s function has a typical sharp peak in the vicinity of the point of action of the point mass source, and in the vicinity of the top boundary of the layer ,the values of the second element of the Green’s function are times higher than the values of the first one the state of which is corresponding to the quick migration way. On this basis the solutions of the initial-boundary value problems under the action of the internal point source of mass are found. The cases of the deterministic source as well as stochastic ones under uniformand triangular distributions of the coordinate of the mass source location are considered.
8
Content available Distributed controllability of one-dimensional heat equation in unbounded domains: The Green's function approach
Khurshudyan Asatur Zh.
Archives of Control Sciences
|
2019
|
Vol. 29, No. 1
57--71
EN
We derive exact and approximate controllability conditions for the linear one-dimensional heat equation in an infinite and a semi-infinite domains. The control is carried out by means of the time-dependent intensity of a point heat source localized at an internal (finite) point of the domain. By the Green’s function approach and the method of heuristic determination of resolving controls, exact controllability analysis is reduced to an infinite system of linear algebraic equations, the regularity of which is sufficient for the existence of exactly resolvable controls. In the case of a semi-infinite domain, as the source approaches the boundary, a lack of L2-null-controllability occurs, which is observed earlier by Micu and Zuazua. On the other hand, in the case of infinite domain, sufficient conditions for the regularity of the reduced infinite system of equations are derived in terms of control time, initial and terminal temperatures. A sufficient condition on the control time, heat source concentration point and initial and terminal temperatures is derived for the existence of approximately resolving controls. In the particular case of a semi-infinite domain when the heat source approaches the boundary, a sufficient condition on the control time and initial temperature providing approximate controllability with required precision is derived.
9
Content available Comparison of heating curves of a rectangular busbar in different conditions of heat abstraction during the short-circuit heating
Zaręba M.
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2018
|
Vol. 66, nr 1
79--85
EN
The paper compares heating curves for a rectangular busbar in the conditions of convective and adiabatic heat transfer during short-circuit heating. Different coefficients of heat transfer from the external surface of the busbar and different busbar cross-sections have been assumed. This has allowed determining the error value occurring when the adiabatic rather than convective boundary condition is presumed at short circuit. The analysis takes into account a change of resistivity in the temperature function. The respective boundary-initial problems have been solved with analytical methods using Green’s function. The calculated results show that no considerable errors occur for long-lasting short circuits with an adiabatic rather than convective boundary condition.
10
Content available Fizyczne podstawy metody interferometrii sejsmicznej
Czarny R.
Zeszyty Naukowe Instytutu Gospodarki Surowcami Mineralnymi i Energią PAN
|
2017
|
nr 101
195--202
PL
Interferometria sejsmiczna jest dynamicznie rozwijającą się metodą, której pierwsze zastosowania sięgają początków obecnego stulecia. Aktualnie znajduje coraz szersze zastosowanie w zagadnieniach m.in. obrazowania głębokich struktur ziemi oraz utworów przypowierzchniowych, monitorowania procesów wulkanicznych oraz analizowania wpływu silnych trzęsień ziemi na obiekty budowlane. Metoda ta pozwala na odtworzenie odpowiedzi impulsowej tzw. funkcji Greena ośrodka pomiędzy parą odbiorników na podstawie zarejestrowanych w tym samym czasie sejsmicznych pól falowych na tych odbiornikach. W wyniku odpowiednich operacji matematycznych metoda ta zamienia zarejestrowane na odbiornikach koherentne fale sejsmiczne o nieznanym czasie oraz miejscu ich wzbudzenia na układ tzw. wirtualnych źródeł emitujących sejsmiczne pole falowe z dowolnego odbiornika. W artykule przedstawiono fizyczne uzasadnienie wyników eksperymentu akustyki odwróconego czasu (ang. time-reversed acoustics) według Derode i in. (2003), które jest zarazem wytłumaczeniem metody interferometrii sejsmicznej. Eksperyment laboratoryjny w pierwszym etapie polegał na rejestracji akustycznego pola falowego wyemitowanego na brzegu naczynia wypełnionego cieczą i stalowymi prętami. Następnie rejestracje zostały odwrócone w czasie i wysłane powtórnie do wewnątrz naczynia i odebrany po przeciwnej stronie. Zarejestrowany na końcu sygnał okazał się zbliżony do sygnału wyemitowanego, pomimo przejścia przez ośrodek wielokrotnie rozpraszający. Doświadczenie to uzasadniono wykorzystując technikę korelacji wzajemnej (ang. cross-correlation), zasadę superpozycji pola falowego oraz zasadę wzajemności Rayleigha.
EN
Seismic interferometry is a geophysical method which has been developing very rapidly over the last decade. It has been applied to image deep structures of the Earth as well as near-surface, monitor volcanic processes, geothermal reservoirs within exploitation, rock mass deformation induced by mining, landslides, ground water storage, ice sheet or the impact of strong earthquakes to buildings. The vast majority of these applications use ambient seismic noise as a seismic source. This method involves reconstructing thte impulse response, the socalled Green’s function, between pair of receivers based on the wave field registered by them. Using seismic interferometry with various data processing flows the registered coherent seismic waves by the receivers can be changed to virtual sources which are placed in the receiver locations. In the article, the physical derivation of the time-reversed acoustics experiment which was introduced by Derode et. al. (2003) is presented. This derivation also explains the seismic interferometry method. The laboratory experiment contained two phases. First, an acoustics signal was emitted into the medium with hundreds of scatterers (cube with liquid and rods) and registered on the opposite side of the medium. Then, registrations were reversed and emitted back. Finally, the wave field refocused exactly in the point of initial excitation. Derode et. al. explain these results using the cross-correlation technique, superposition and Rayleigh’s reciprocity principles.
11
Content available remote Free Vibrations of a Rectangular Plate Elastically Connected with Beams
Kukla S.
Vibrations in Physical Systems
|
2004
|
Vol. 21
235--238
first rewind previous Strona / 1 next fast forward last
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.