Geodesic
On self-similar solutions to the surface diffusion flow equations with contact angle boundary conditions
Tomoro Asai1 ; Yoshikazu Giga1
1University of Tokyo, Japan
Interfaces and free boundaries, Tome 16 (2014) no. 4, pp. 539-573

Voir la notice de l'article provenant de la source EMS Press

DOI

We consider the surface diffusion flow equation when the curve is given as the graph of a function v(x,t) defined in a half line R+={x>0} under the boundary conditions vx​=tanβ>0 and vxxx​=0 at x=0. We construct a unique (spatially bounded) self-similar solution when the angle β is sufficiently small. We further prove the stability of this self-similar solution. The problem stems from an equation proposed by W. W. Mullins (1957) to model formation of surface grooves on the grain boundaries, where the second boundary condition vxxx​=0 is replaced by zero slope condition on the curvature of the graph.
DOI : 10.4171/ifb/329
Classification : 35-XX, 74-XX
Mots-clés : Self-similar solution, surface diffusion flow, stability, analytic semigroup, mild solution

Tomoro Asai  1   ; Yoshikazu Giga  1

1 University of Tokyo, Japan 
Tomoro Asai; Yoshikazu Giga. On self-similar solutions to the surface diffusion flow equations with contact angle boundary conditions. Interfaces and free boundaries, Tome 16 (2014) no. 4, pp. 539-573. doi: 10.4171/ifb/329
@article{10_4171_ifb_329,
     author = {Tomoro Asai and Yoshikazu Giga},
     title = {On self-similar solutions to the surface diffusion flow equations with contact angle boundary conditions},
     journal = {Interfaces and free boundaries},
     pages = {539--573},
     year = {2014},
     volume = {16},
     number = {4},
     doi = {10.4171/ifb/329},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/329/}
}
TY  - JOUR
AU  - Tomoro Asai
AU  - Yoshikazu Giga
TI  - On self-similar solutions to the surface diffusion flow equations with contact angle boundary conditions
JO  - Interfaces and free boundaries
PY  - 2014
SP  - 539
EP  - 573
VL  - 16
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4171/ifb/329/
DO  - 10.4171/ifb/329
ID  - 10_4171_ifb_329
ER  - 
%0 Journal Article
%A Tomoro Asai
%A Yoshikazu Giga
%T On self-similar solutions to the surface diffusion flow equations with contact angle boundary conditions
%J Interfaces and free boundaries
%D 2014
%P 539-573
%V 16
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4171/ifb/329/
%R 10.4171/ifb/329
%F 10_4171_ifb_329

Cité par Sources :