Displaying similar documents to “Blow-up results for a nonlinear hyperbolic equation with Lewis function.”

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

Qingyong Gao, Fushan Li, Yanguo Wang (2011)

Open Mathematics

Similarity:

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.

Global in time solvability of the initial boundary value problem for some nonlinear dissipative evolution equations

Yoshihiro Shibata (1993)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

The global in time solvability of the one-dimensional nonlinear equations of thermoelasticity, equations of viscoelasticity and nonlinear wave equations in several space dimensions with some boundary dissipation is discussed. The blow up of the solutions which might be possible even for small data is excluded by allowing for a certain dissipative mechanism.

Existence and non-existence of global solutions for nonlinear hyperbolic equations of higher order

Guo Wang Chen, Shu Bin Wang (1995)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

The existence and uniqueness of classical global solution and blow up of non-global solution to the first boundary value problem and the second boundary value problem for the equation u t t - α u x x - β u x x t t = ϕ ( u x ) x are proved. Finally, the results of the above problem are applied to the equation arising from nonlinear waves in elastic rods u t t - a 0 + n a 1 ( u x ) n - 1 u x x - a 2 u x x t t = 0 .