Time-periodic solutions of advection-diffusion equations on moving hypersurfaces

TL;DR

This paper investigates the existence and uniqueness of time-periodic solutions to advection-diffusion equations on moving hypersurfaces, providing mathematical proofs within appropriate function spaces.

Contribution

It establishes the existence and uniqueness of solutions for advection-diffusion equations on periodically moving hypersurfaces, a novel extension in the mathematical analysis of such PDEs.

Findings

Proved existence of solutions in H"older spaces

Established uniqueness of solutions

Applied to periodically moving hypersurfaces

Abstract

In this paper we study time-periodic solutions to advection-diffusion equations of a scalar quantity $u$ on a periodically moving $n$-dimensional hypersurface $\Gamma(t) \subset \mathbb{R}^{n+1}$. We prove existence and uniqueness of solutions in suitable H\"older spaces.