Dynamics of nonlinear hyperbolic equations of Kirchhoff type

Speaker

Zhitao Zhang , Academy of Mathematics and Systems Science, Chinese Academy of Sciences

Time

25 Oct, 10:15 - 10:55

Abstract

We study the initial boundary value problem of the important hyperbolic Kirchhoff equation

$$\partial_{tt} u-\left(a\int_\Omega |\nabla u|^2 dx +b \right) \Delta u =\lambda u +|u|^{p-1}u, \,\, u(t, x)|_{\partial \Omega} =0,$$

where a, b>0, p>1, λ and the initial energy is arbitrarily large. We prove several new theorems on the dynamics such as the boundedness or finite time blow-up of solution under the different range of a, b, λ and the initial data.