Blow up, global existence and growth rate estimates in nonlinear parabolic systems

Rencławowicz, Joanna

Colloquium Mathematicae, Tome 84/85 (2000), p. 43-66 / Harvested from The Polish Digital Mathematics Library

Résumé

We prove Fujita-type global existence and nonexistence theorems for a system of m equations (m > 1) with different diffusion coefficients, i.e. $u_{i t} - d_{i} Δ u_{i} = \prod_{k = 1}^{m} u_{k}^{p_{k}^{i}}, i = 1, . . ., m, x \in ℝ^{N}, t > 0,$ with nonnegative, bounded, continuous initial values and $p_{k}^{i} \geq 0$ , $i, k = 1, . . ., m$ , $d_{i} > 0$ , $i = 1, . . ., m$ . For solutions which blow up at $t = T < \leq \infty$ , we derive the following bounds on the blow up rate: $u_{i} (x, t) \leq C {(T - t)}^{- α_{i}}$ with C > 0 and $α_{i}$ defined in terms of $p_{k}^{i}$ .

Publié le : 2000-01-01

Zbl 0959.35084

EUDML-ID : urn:eudml:doc:210841

@article{bwmeta1.element.bwnjournal-article-cmv86i1p43bwm,
     author = {Joanna Renc\l awowicz},
     title = {Blow up, global existence and growth rate estimates in nonlinear parabolic systems},
     journal = {Colloquium Mathematicae},
     volume = {84/85},
     year = {2000},
     pages = {43-66},
     zbl = {0959.35084},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv86i1p43bwm}
}

Rencławowicz, Joanna. Blow up, global existence and growth rate estimates in nonlinear parabolic systems. Colloquium Mathematicae, Tome 84/85 (2000) pp. 43-66. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv86i1p43bwm/

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