A note on existence and uniqueness of solutions for a 2D bioheat problem

Abstract

We consider a 2D bioheat model on a domain with curvilinear polygonal boundary and boundary conditions involving heat transfer between blood vessels and tissue. Based on elliptic regularity on polygons and semigroup theory, we obtain a Fourier series representation for the solution in settings. The results become useful in that they provide theoretical support for numerical approaches recently published in the literature.

Keywords:

• Pennes equation
• bioheat transfer
• Fourier series
• curvilinear polygons

AMS Subject Classifications:

• 35Q92
• 65M70
• 35P15

Acknowledgements

The authors are indebted to anonymous reviewers for providing suggestions that improved significantly the presentation of this work.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work of the second author is supported by CNPq, Brazil [grant number 308709/2011-0], [grant number 477093/2011-6].