Blow up, global existence and growth rate estimates in nonlinear parabolic systems
Colloquium Mathematicum, Tome 86 (2000) no. 1, pp. 43-66
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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 $p_k^i$.
Keywords:
invariant manifold, reaction-diffusion system, invariant region, global existence, blow up
Joanna Rencławowicz. Blow up, global existence and growth rate estimates in nonlinear parabolic systems. Colloquium Mathematicum, Tome 86 (2000) no. 1, pp. 43-66. doi: 10.4064/cm-86-1-43-66
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author = {Joanna Renc{\l}awowicz},
title = {Blow up, global existence and growth rate estimates in nonlinear parabolic systems},
journal = {Colloquium Mathematicum},
pages = {43--66},
year = {2000},
volume = {86},
number = {1},
doi = {10.4064/cm-86-1-43-66},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm-86-1-43-66/}
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