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

• Autorzy: Qingyong Gao , Fushan Li , Yanguo Wang
• Języki publikacji: EN

Abstrakty

EN

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

Słowa kluczowe

EN

Blow-up; Nonlinear Kirchhoff-type equation; Positive upper bounded initial energy

Kategorie tematyczne

• 35L70: Nonlinear second-order hyperbolic equations
• 35L35: Initial-boundary value problems for higher-order hyperbolic equations

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2011
• Tom: 9
• Numer: 3
• Strony: 686-698

Daty

wydano

2011-06-01

online

2011-03-22

Twórcy

autor

Qingyong Gao

• Qufu Normal University

autor

Fushan Li

• Qufu Normal University

autor

Yanguo Wang

• Qufu Normal University

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-010-0096-2