Blow-up of the solution for higher-order Kirchhoff-type equations with nonlinear dissipation

Qingyong Gao; Fushan Li; Yanguo Wang

Open Mathematics, Tome 9 (2011), p. 686-698 / Harvested from The Polish Digital Mathematics Library

Résumé

In this paper, we consider the nonlinear Kirchhoff-type equation $u_{t t} + M ({∥D^{m} u (t)∥}_{2}^{2}) {(- Δ)}^{m} u + {|u_{t}|}^{q - 2} u_{t} = {|u_{t}|}^{p - 2} u$ with initial conditions and homogeneous boundary conditions. Under suitable conditions on the initial datum, we prove that the solution blows up in finite time.

Publié le : 2011-01-01

Zbl 1233.35145

EUDML-ID : urn:eudml:doc:269597

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     author = {Qingyong Gao and Fushan Li and Yanguo Wang},
     title = {Blow-up of the solution for higher-order Kirchhoff-type equations with nonlinear dissipation},
     journal = {Open Mathematics},
     volume = {9},
     year = {2011},
     pages = {686-698},
     zbl = {1233.35145},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-010-0096-2}
}

Qingyong Gao; Fushan Li; Yanguo Wang. Blow-up of the solution for higher-order Kirchhoff-type equations with nonlinear dissipation. Open Mathematics, Tome 9 (2011) pp. 686-698. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-010-0096-2/

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