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

Miskolc Mathematical Notes

article

Tugrul Cömert¹  Erhan Piskin¹ 

[1] Dicle University, Department of Mathematics

关键词: higher-order parabolic equation;    global existence;    logarithmic nonlinearity;   

DOI  :  10.18514/MMN.2022.3894

学科分类：数学（综合）

来源: Miskolci Egyetem

【 摘 要 】

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.

【 授权许可】

CC BY