Finite time blow up of solutions of the Kirchhoff-type equation with variable exponents

In this work, we investigate the following Kirchhoff-type equation with variable exponent nonlinearitiesu_{tt}-M(‖∇u‖²)△u+|u_{t}|^{p(x)-۲}u_{t}=|u|^{q(x)-۲}u.We proved the blow up of solutions in finite time by using modified energy functional method.

کلیدواژه ها:

Blow up ، Kirchhoff-type equation ، Variable exponent