Sharp interface limit of the convective Allen-Cahn equation in high dimensional spaces

Key Points

• The sharp interface limit of the convective allen-cahn equation is derived rigorously, demonstrating significant relationships with transport dynamics.
• Utilizing matched asymptotic expansions, results are extended to high dimensional spaces, showcasing increased complexity in solutions.
• Initial conditions and smooth velocity fields are crucial for establishing the sharp interface limit, reinforcing mathematical foundations.
• This work builds upon previous research by Abels, expanding the understanding of convective dynamics in higher dimensions.