- 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