open access

https://doi.org/10.14943/2115.98992

https://hdl.handle.net/2115/98992

Asymptotically self-similar graph-like solutions to a multi-dimensional surface diffusion flow equation under contact angle and no-flux boundary conditions : In the memory of Professor Louis Nirenberg – a founding father of modern PDE theory

英語

2026-03-11

Department of Mathematics,Hokkaido University

Hokkaido University Preprint Series in Mathematics

1165(1)

1-29

This paper studies Mullins’ model of thermal grooving which consists of a surface diffusion flow equation with contact angle and no-flux boundary conditions. We consider this problem in a multi-dimensional half space and prove that if the slope of the initial data is close to that consistent with the contact angle, then there exists a unique globalin- time solution. In particular, we show the existence of a self-similar solution for a given behavior at the space infinity. We also show that our global solution converges to a self-similar solution as the time tends to infinity if the initial data is asymptotically homogeneous at the space infinity. No assumption on the size of the contact angle is imposed.

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