VSE knjižnice (vzajemna bibliografsko-kataložna baza podatkov COBIB.SI)
  • Turing patterns in general reaction-diffusion systems of Brusselator type
    Ghergu, Marius ; Rǎdulescu, Vicenţiu, 1958-
    We study the reaction-diffusion system ▫$$ \left\{\begin{aligned} &u_t - d_1\Delta u = a-(b+1)u + f(u)v &&\mbox{ in } \Omega\times (0,T),\\ &v_t - d_2\Delta v = bu - f(u)v &&\mbox{ in } \Omega\times ... (0,T),\\ &u(x,0) = u_0(x),v(x,0) = v_0(x)&& \mbox{ on }\Omega,\\ &\frac{\partial u}{\partial \nu}(x,t) = \frac{\partial u}{\partial \nu}(x,t) = 0&&\mbox{ on } \partial \Omega \times(0,T). \end{aligned}\right.$$▫ Here ▫$\Omega$▫ is a smooth and bounded domain in ▫${\mathbb R}^N$▫ (▫$N \geq 1$▫), ▫$a,b,d_1,d_2>0$▫ and ▫$f \in C^1[0,\infty)$▫ is a non-decreasing function. The case ▫$f(u)=u^2$▫ corresponds to the standard Brusselator model for autocatalytic oscillating chemical reactions. Our analysis points out the crucial role played by the nonlinearity ▫$f$▫ in the existence of Turing patterns. More precisely we show that if ▫$f$▫ has a sublinear growth then no Turing patterns occur, while if ▫$f$▫ has a superlinear growth then existence of such patterns is strongly related to the inter-dependence between the parameters ▫$a,b$▫ and the diffusion coefficients ▫$d_1, d_2$▫.
    Vir: Communications in contemporary mathematics. - ISSN 0219-1997 (Vol. 12, no. 4, 2010, str. 661-679)
    Vrsta gradiva - članek, sestavni del
    Leto - 2010
    Jezik - angleški
    COBISS.SI-ID - 15662681

    Povezava(-e):

    http://dx.doi.org/10.1142/S0219199710003968

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