TY - JOUR
T1 - Stability and instability of group invariant asymptotic profiles for fast diffusion equations
AU - Akagi, Goro
N1 - Funding Information:
Acknowledgements This work is partially supported by KAKENHI #22740093 and Hyogo Science and Technology Association.
Publisher Copyright:
© 2013, Springer-Verlag Italia.
PY - 2013
Y1 - 2013
N2 - This paper is concerned with group invariant solutions for fast diffusion equations in symmetric domains. First, it is proved that the group invariance of weak solutions is inherited from initial data. After briefly reviewing previous results on asymptotic profiles of vanishing solutions and their stability, the notions of stability and instability of group invariant profiles are introduced under a similarly invariant class of perturbations, and moreover, some stability criteria are exhibited and applied to symmetric domain (e.g., annulus) cases.
AB - This paper is concerned with group invariant solutions for fast diffusion equations in symmetric domains. First, it is proved that the group invariance of weak solutions is inherited from initial data. After briefly reviewing previous results on asymptotic profiles of vanishing solutions and their stability, the notions of stability and instability of group invariant profiles are introduced under a similarly invariant class of perturbations, and moreover, some stability criteria are exhibited and applied to symmetric domain (e.g., annulus) cases.
KW - Asymptotic profile
KW - Fast diffusion equation
KW - Group invariance
KW - Stability
UR - http://www.scopus.com/inward/record.url?scp=84975177927&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84975177927&partnerID=8YFLogxK
U2 - 10.1007/978-88-470-2841-8_1
DO - 10.1007/978-88-470-2841-8_1
M3 - Article
AN - SCOPUS:84975177927
SN - 2281-518X
VL - 2
SP - 1
EP - 16
JO - Springer INdAM Series
JF - Springer INdAM Series
ER -