Solution estimates for one class of elliptic and parabolic nonlinear equations

Abstract

In this paper, we provide an alternative proof of the separation theorem, which can be easily extended to a certain class of systems of elliptic and parabolic nonlinear equations in non-reflexive spaces.

Keywords:

• Separation
• elliptic nonlinear operator
• parabolic nonlinear operator
• non-reflexive spaces

AMS Subject Classifications:

• 35J87
• 35J88
• 35K86
• 35K87

Acknowledgments

The authors thank the anonymous referees for reading the paper carefully and providing thoughtful comments, which improved the exposition of the paper.

Disclosure statement

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

Additional information

Funding

The first author was supported by the grant no. AP14971679 of the Science Committee of the Ministry of Education and Science of the Republic of Kazakhstan.