Existence of nonnegative solutions for parabolic problem on Dirichlet forms

ABSTRACT

In this work, we investigate perturbed parabolic problem on measure spaces. For strongly local Dirichlet form, we obtain some results on existence and uniqueness of nonnegative solution. We also presented some examples as an applications.

KEYWORDS:

• Heat equation
• Dirichlet form
• the standard parabolic theory

AMS SUBJECT CLASSIFICATIONS:

• 35J35
• 35J50
• 35J60

Acknowledgements

I would like to thank the referee for carefully reading this paper and providing useful comments.

Disclosure statement

No potential conflict of interest was reported by the author.