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

100%

Gao Q., Li F., Wang Y.

Open Mathematics

2011

tom 9

nr 3

686-698

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.

Blow-up of solutions for a viscoelastic equation with nonlinear damping

100%

Zhifeng Y.

Open Mathematics

2008

tom 6

nr 4

568-575

The initial boundary value problem for a viscoelastic equation with nonlinear damping in a bounded domain is considered. By modifying the method, which is put forward by Li, Tasi and Vitillaro, we sententiously proved that, under certain conditions, any solution blows up in finite time. The estimates of the life-span of solutions are also given. We generalize some earlier results concerning this equation.

Ograniczanie wyników

2 Open Mathematics

1 Gao Q.

1 Li F.

1 Wang Y.

1 Zhifeng Y.

1 2011

1 2008

Wyniki wyszukiwania

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

Blow-up of solutions for a viscoelastic equation with nonlinear damping