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

Qingyong Gao; Fushan Li; Yanguo Wang

Open Mathematics (2011)

- Volume: 9, Issue: 3, page 686-698
- ISSN: 2391-5455

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topQingyong Gao, Fushan Li, and Yanguo Wang. "Blow-up of the solution for higher-order Kirchhoff-type equations with nonlinear dissipation." Open Mathematics 9.3 (2011): 686-698. <http://eudml.org/doc/269597>.

@article{QingyongGao2011,

abstract = {In this paper, we consider the nonlinear Kirchhoff-type equation \[ u\_\{tt\} + M(\left\Vert \{D^m u(t)\} \right\Vert \_2^2 )( - \Delta )^m u + \left| \{u\_t \} \right|^\{q - 2\} u\_t = \left| \{u\_t \} \right|^\{p - 2\} u \]
with initial conditions and homogeneous boundary conditions. Under suitable conditions on the initial datum, we prove that the solution blows up in finite time.},

author = {Qingyong Gao, Fushan Li, Yanguo Wang},

journal = {Open Mathematics},

keywords = {Blow-up; Nonlinear Kirchhoff-type equation; Positive upper bounded initial energy; nonlinear Kirchhoff-type equation; positive upper bounded initial energy; homogeneous boundary conditions},

language = {eng},

number = {3},

pages = {686-698},

title = {Blow-up of the solution for higher-order Kirchhoff-type equations with nonlinear dissipation},

url = {http://eudml.org/doc/269597},

volume = {9},

year = {2011},

}

TY - JOUR

AU - Qingyong Gao

AU - Fushan Li

AU - Yanguo Wang

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

JO - Open Mathematics

PY - 2011

VL - 9

IS - 3

SP - 686

EP - 698

AB - In this paper, we consider the nonlinear Kirchhoff-type equation \[ u_{tt} + M(\left\Vert {D^m u(t)} \right\Vert _2^2 )( - \Delta )^m u + \left| {u_t } \right|^{q - 2} u_t = \left| {u_t } \right|^{p - 2} u \]
with initial conditions and homogeneous boundary conditions. Under suitable conditions on the initial datum, we prove that the solution blows up in finite time.

LA - eng

KW - Blow-up; Nonlinear Kirchhoff-type equation; Positive upper bounded initial energy; nonlinear Kirchhoff-type equation; positive upper bounded initial energy; homogeneous boundary conditions

UR - http://eudml.org/doc/269597

ER -

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