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    Wyświetlanie 1-9 z 9
    Tytuł:
    A Classical Approach to Dynamics of Parabolic Competitive Systems
    Autorzy:
    Pietruk, Małgorzata
    Przeradzki, Bogdan
    Powiązania:
    https://bibliotekanauki.pl/articles/44444333.pdf
    Data publikacji:
    2010
    Wydawca:
    Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
    Tematy:
    Reaction-diffusion system
    competition.
    Opis:
    We study the reaction-diffusion system, its stationary solutions, the behavior of the system near them and discuss similarities and differences for different boundary conditions.
    Źródło:
    Acta Universitatis Lodziensis. Folia Mathematica; 2010, 17; 23-38
    2450-7652
    Pojawia się w:
    Acta Universitatis Lodziensis. Folia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Global existence and blow up of solutions for a completely coupled Fujita type system of reaction-diffusion equations
    Autorzy:
    Rencławowicz, Joanna
    Powiązania:
    https://bibliotekanauki.pl/articles/1338982.pdf
    Data publikacji:
    1998
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    reaction-diffusion system
    global existence
    blow up
    Opis:
    We examine the parabolic system of three equations $u_t$ - Δu = $v^p$, $v_t$ - Δv = $w^q$, $w_t$ - Δw = $u^r$, x ∈ $ℝ^N$, t > 0 with p, q, r positive numbers, N ≥ 1, and nonnegative, bounded continuous initial values. We obtain global existence and blow up unconditionally (that is, for any initial data). We prove that if pqr ≤ 1 then any solution is global; when pqr > 1 and max(α,β,γ) ≥ N/2 (α, β, γ are defined in terms of p, q, r) then every nontrivial solution exhibits a finite blow up time.
    Źródło:
    Applicationes Mathematicae; 1998-1999, 25, 3; 313-326
    1233-7234
    Pojawia się w:
    Applicationes Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Global pointwise a priori bounds and large time behaviour for a nonlinear system describing the spread of infectious disease
    Autorzy:
    Kirane, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/1340654.pdf
    Data publikacji:
    1993
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    global existence
    nonlinear reaction-diffusion system
    large time behaviour
    Opis:
    This paper considers a reaction-diffusion system with biatic diffusion.Existence of a globally bounded solution is proved and its large timebehaviour is given.
    Źródło:
    Applicationes Mathematicae; 1993-1995, 22, 1; 1-9
    1233-7234
    Pojawia się w:
    Applicationes Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Blow up, global existence and growth rate estimates in nonlinear parabolic systems
    Autorzy:
    Rencławowicz, Joanna
    Powiązania:
    https://bibliotekanauki.pl/articles/965693.pdf
    Data publikacji:
    2000
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    invariant manifold
    reaction-diffusion system
    invariant region
    global existence
    blow up
    Opis:
    We prove Fujita-type global existence and nonexistence theorems for a system of m equations (m > 1) with different diffusion coefficients, i.e. $u_{it} - d_{i} Δu_{i} = \prod_{k=1}^m u_{k}^{p_k^i}, i=1,...,m, x ∈ ℝ^{N}, t > 0,$ with nonnegative, bounded, continuous initial values and $p_{k}^{i} ≥ 0$, $i,k = 1,...,m$, $d_i > 0$, $i = 1,...,m$. For solutions which blow up at $t = T <≤ ∞$, we derive the following bounds on the blow up rate: $u_i(x,t) ≤ C(T - t)^{-α_{i}}$ with C > 0 and $α_i$ defined in terms of $p_k^i$.
    Źródło:
    Colloquium Mathematicum; 2000, 86, 1; 43-66
    0010-1354
    Pojawia się w:
    Colloquium Mathematicum
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Synchronization of FitzHugh-Nagumo reaction-diffusion systems via one-dimensional linear control law
    Autorzy:
    Ouannas, Adel
    Mesdoui, Fatiha
    Momani, Shaher
    Batiha, Iqbal
    Grassi, Giuseppe
    Powiązania:
    https://bibliotekanauki.pl/articles/1409370.pdf
    Data publikacji:
    2021
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    FitzHugh-Nagumo
    synchronization
    uni-dimensional control
    linear control
    reaction-diffusion system
    neuronal networks
    Lyapunov’s second method
    Opis:
    The Fitzhugh-Nagumo model (FN model), which is successfully employed in modeling the function of the so-called membrane potential, exhibits various formations in neuronal networks and rich complex dynamics. This work deals with the problem of control and synchronization of the FN reaction-diffusion model. The proposed control law in this study is designed to be uni-dimensional and linear law for the purpose of reducing the cost of implementation. In order to analytically prove this assertion, Lyapunov’s second method is utilized and illustrated numerically in one- and/or two-spatial dimensions.
    Źródło:
    Archives of Control Sciences; 2021, 31, 2; 333-345
    1230-2384
    Pojawia się w:
    Archives of Control Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Behaviour of global solutions for a system of reaction-diffusion equations from combustion theory
    Autorzy:
    Badraoui, Salah
    Powiązania:
    https://bibliotekanauki.pl/articles/1338841.pdf
    Data publikacji:
    1999
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    global existence
    boundedness
    reaction-diffusion equations
    large time behaviour
    Opis:
    We are concerned with the boundedness and large time behaviour of the solution for a system of reaction-diffusion equations modelling complex consecutive reactions on a bounded domain under homogeneous Neumann boundary conditions. Using the techniques of E. Conway, D. Hoff and J. Smoller [3] we also show that the bounded solution converges to a constant function as t → ∞. Finally, we investigate the rate of this convergence.
    Źródło:
    Applicationes Mathematicae; 1999, 26, 2; 133-150
    1233-7234
    Pojawia się w:
    Applicationes Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A robust computational technique for a system of singularly perturbed reaction–diffusion equations
    Autorzy:
    Kumar, V.
    Bawa, R. K.
    Lal, A. K.
    Powiązania:
    https://bibliotekanauki.pl/articles/330202.pdf
    Data publikacji:
    2014
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    asymptotic expansion approximation
    backward difference operator
    trapezoidal method
    piecewise uniform Shishkin mesh
    rozwinięcie asymptotyczne
    operator różnicowy
    metoda trapezowa
    Opis:
    In this paper, a singularly perturbed system of reaction–diffusion Boundary Value Problems (BVPs) is examined. To solve such a type of problems, a Modified Initial Value Technique (MIVT) is proposed on an appropriate piecewise uniform Shishkin mesh. The MIVT is shown to be of second order convergent (up to a logarithmic factor). Numerical results are presented which are in agreement with the theoretical results.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2014, 24, 2; 387-395
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Numerical study on extraction of tritium generated in HMR by way of system composed of EXEL-process and thermal diffusion column cascade
    Autorzy:
    Shimizu, M.
    Takeshita, K.
    Powiązania:
    https://bibliotekanauki.pl/articles/146995.pdf
    Data publikacji:
    2002
    Wydawca:
    Instytut Chemii i Techniki Jądrowej
    Tematy:
    chemical exchange reaction
    heavy water
    isotope separation
    thermal diffusion
    trickel-bed reactor
    tritium
    Opis:
    A new tritium extraction system composed of a trickle-bed hydrogen/water isotopic exchange column using a hydrophobic Pt-catalyst combined with an SPE-water electrolyser (EXEL-process) and a thermal diffusion column cascade was proposed for the removal of tritium from heavy water irradiated in HMR ((Heavy Water Moderated Power Reactor), volume of heavy water = 140 m3 and mean neutron flux = 5×1013 n/cm2s). Numerical study on the extraction of tritium from the heavy water was carried out and the dimensions of proposed system were determined under the conditions that the concentration of tritium in the heavy water was kept less than 2.5 Ci/lHW. The calculation results indicated that the proposed system was designed practically.
    Źródło:
    Nukleonika; 2002, 47,suppl.1; 89-93
    0029-5922
    1508-5791
    Pojawia się w:
    Nukleonika
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Front Dynamics with Time Delays in a Bistable System of the Reaction-Diffusion Type: Role of the Symmetry of the Rate Function
    Autorzy:
    Bakanas, R.
    Ivanauskas, F.
    Jasaitis, V.
    Powiązania:
    https://bibliotekanauki.pl/articles/1505296.pdf
    Data publikacji:
    2011-03
    Wydawca:
    Polska Akademia Nauk. Instytut Fizyki PAN
    Tematy:
    05.45.-a
    02.30.Jr
    82.40.Ck
    Opis:
    The retardation effects in dynamics of the ac driven "bistable" fronts joining two states of the different stability in a bistable system of the reaction-diffusion type are investigated by use of the macroscopic kinetic equation of the reaction kinetics. We approximate the rate (reaction) function in the governing equation of "bistable" fronts by the piecewise linear dependence of the flexible symmetry, encompassing both cases of the symmetrical and asymmetrical rate functions. By numerically simulating the drift motion of the ac driven front being subjected to the time-dependent step-like (rectangular) forcing we investigate the lag time between the ac force and the instantaneous velocity of the ac driven front. We find that the time lags derivable by the symmetrical and asymmetrical rate functions notably differ, namely, we show that (a) the lag time is a function of the outer slope coefficients of the rate function and is not sensitive to the inner, (b) it has only weak dependence on the strength of the applied forcing, (c) the retardation effects (time lags) in the front dynamics are describable adequately enough by use of the perturbation theory. Another aspect of the front dynamics discussed in this report is the influence of the retardation effects on the ratchet-like transport of the ac driven fronts being described by the asymmetrical rate functions of the "low" symmetry. By considering the response of "bistable" front to the single-harmonic ac force we find that the occurrence of the time lags in the oscillatory motion of the ac driven front shrink the spurious drift of the front; the spurious drift practically disappears if the frequency of the oscillatory force significantly exceeds the characteristic relaxation rate of the system. Furthermore, the occurrence of the time lags in the front dynamics leads to the vanishing of the reversals in the directed net motion of the ac driven fronts, being always inherent in the case of the slow (quasi-stationary) ac drive, i.e., the possibilities of controlling the directed net motion of the self-ordered fronts by the low- and high-frequency zero-mean ac forces radically differ.
    Źródło:
    Acta Physica Polonica A; 2011, 119, 3; 282-297
    0587-4246
    1898-794X
    Pojawia się w:
    Acta Physica Polonica A
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-9 z 9

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