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

Document Type : Research Paper

Author

Dicle University, Department of Mathematics

Abstract

In this work, we investigate the following Kirchhoff-type equation with variable exponent nonlinearities

$u_{tt}-M(‖∇u‖²)△u+|u_{t}|^{p(x)-2}u_{t}=|u|^{q(x)-2}u.$

We proved the blow up of solutions in finite time by using modified energy functional method.

Keywords