Document Type : Research Paper

Author

• Erhan Pişkin

Dicle University, Department of Mathematics, 21280 Diyarbakır, Turkey

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 the modified energy functional method.

Keywords

• Blow up
• Kirchhoff-type equation
• Variable exponent