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.
Pişkin,E . (2020). Finite time blow up of solutions of the Kirchhoff-type equation with variable exponents. International Journal of Nonlinear Analysis and Applications, 11(1), 37-45. doi: 10.22075/ijnaa.2019.16022.1841
MLA
Pişkin,E . "Finite time blow up of solutions of the Kirchhoff-type equation with variable exponents", International Journal of Nonlinear Analysis and Applications, 11, 1, 2020, 37-45. doi: 10.22075/ijnaa.2019.16022.1841
HARVARD
Pişkin E. (2020). 'Finite time blow up of solutions of the Kirchhoff-type equation with variable exponents', International Journal of Nonlinear Analysis and Applications, 11(1), pp. 37-45. doi: 10.22075/ijnaa.2019.16022.1841
CHICAGO
E Pişkin, "Finite time blow up of solutions of the Kirchhoff-type equation with variable exponents," International Journal of Nonlinear Analysis and Applications, 11 1 (2020): 37-45, doi: 10.22075/ijnaa.2019.16022.1841
VANCOUVER
Pişkin E. Finite time blow up of solutions of the Kirchhoff-type equation with variable exponents. IJNAA. 2020;11(1):37-45. doi: 10.22075/ijnaa.2019.16022.1841
International Journal of Nonlinear Analysis and Applications