New critical curves for a doubly degenerate parabolic equation in half-line

Abstract

This article considers a doubly degenerate parabolic equation with weighted nonlocal sources and nonlinear boundary flux in half-line. We establish the new critical global existence curve and critical Fujita curve by constructing various modified self-similar super- and sub-solutions under appropriate conditions.

Keywords:

• Doubly degenerate parabolic equation
• weighted nonlocal sources
• nonlinear boundary flux
• critical curves

2010 MSCs:

• 35K65
• 35B33
• 35B40

Acknowledgments

This work is supported by the Natural Science Foundation of Shandong Province of China (No.ZR2019MA072) and the Fundamental Research Funds for the Central Universities (No.201964008). The authors would like to deeply thank all the reviewers for their insightful and constructive comments.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is supported by the Natural Science Foundation of Shandong Province of China [No. ZR2019MA072] and the Fundamental Research Funds for the Central Universities [No. 201964008].