Study of weak solutions for a higher order nonlinear degenerate parabolic equation

Abstract

In this paper, we study the existence of weak solutions for a sixth-order nonlinear parabolic equation, which arises in oil–water–surfactant mixtures. Based on the Schauder-type estimates, we establish the global existence of classical solutions for regularized problems. After establishing some necessary uniform estimates on the approximate solutions, we prove the existence of weak solutions. The nonnegativity and the monotonicity of support of solutions are also discussed.

Keywords:

• sixth-order nonlinear parabolic equation
• degenerate
• existence
• nonnegativity

AMS Subject Classifications:

• 35G25
• 35K55
• 35K65

Acknowledgements

The authors would like to express their profound thanks to the referees for valuable suggestions for the revision and improvement of the manuscript.

Notes

No potential conflict of interest was reported by the authors.