Abstract
This paper deals with the asymptotic behavior for a porous medium equation with weighted inner source terms and a nonlinear nonlocal boundary condition. We find the influences of spacetime-varying weight functions and competitive relationship between the multiple nonlinearities on whether determining blow-up of solutions or not, and establish the blow-up rate estimate under some appropriate conditions. Especially, our results include the situation of slow, linear and fast diffusion.
Funding Statement
This work is supported by the Natural Science Foundation of Shandong Province of China (No. ZR2019MA072).
Acknowledgments
The authors would like to deeply thank all the reviewers for their insightful and constructive comments.
Citation
Wentao Huo. Chenyuan Jia. Zhong Bo Fang. "On a Porous Medium Equation with Weighted Inner Source Terms and a Nonlinear Nonlocal Boundary Condition." Taiwanese J. Math. 28 (4) 767 - 797, August, 2024. https://doi.org/10.11650/tjm/240304
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