Regularity of the free boundary in an unstable parabolic problem

TL;DR

This paper investigates the regularity of the free boundary in an unstable parabolic problem related to combustion, demonstrating that it is a $C^{1,rac{eta}{2}}$ hypersurface under certain conditions.

Contribution

It establishes the $C^{1,rac{eta}{2}}$ regularity of the free boundary in an unstable combustion model, advancing understanding of free boundary behavior in such problems.

Findings

Free boundary is a $C^{1,rac{eta}{2}}$ hypersurface.

Proves regularity in an unstable parabolic combustion model.

Provides mathematical foundation for free boundary smoothness.

Abstract

We study the free boundary in an unstable parabolic problem arising from a model in combustion. We consider the physical situation in which the heat advances and prove that the free boundary is a $C^{1,\alpha/2}$ hypersurface.