MMN-3894

# Global existence and exponential decay of solutions for higher-order parabolic equation with logarithmic nonlinearity

• Tugrul Cömert, Dicle University, Department of Mathematics, 21280 Diyarbakir, Turkey, tugrulcomertt@gmail.com
• Erhan Piskin, Dicle University, Department of Mathematics, 21280 Diyarbakir, Turkey, episkin@dicle.edu.tr

## Abstract

This paper deal with the initial boundary value problem for a higher-order parabolic equation with logarithmic source term u_{t}+(-\Delta )^{m}u=u^{r-2}u\ln\left\vert u\right\vert. We show that the global existence of weak solution, by employing the potential wells technique. Also, we obtain the exponential decay for the weak solutions.

Vol. 23 (2022), No. 2, pp. 595-605
DOI: 10.18514/MMN.2022.3894