TY - JOUR
T1 - Critical exponents for the fast diffusion equation with a nonlinear boundary condition
AU - Sato, Ryuichi
AU - Takahashi, Jin
N1 - Funding Information:
The first author was supported by JSPS KAKENHI Grant Number 18K13435 . The second author was supported by JSPS KAKENHI Grant Number 19K14567 .
Publisher Copyright:
© 2019 Elsevier Inc.
PY - 2020/2/1
Y1 - 2020/2/1
N2 - In this paper we consider the fast diffusion equation ∂tu=Δ(um) (x∈Ω, t>0) with a nonlinear boundary condition ∂νum=up (x∈∂Ω, t>0), where 00, Ω⊂RN is a smooth domain and N≥1. We prove that p0=(m+1)/2 is the critical global existence exponent for the cases Ω=RN∖B1‾ (N≥2) and Ω=B1:={x∈RN:|x|<1} (N≥1).
AB - In this paper we consider the fast diffusion equation ∂tu=Δ(um) (x∈Ω, t>0) with a nonlinear boundary condition ∂νum=up (x∈∂Ω, t>0), where 00, Ω⊂RN is a smooth domain and N≥1. We prove that p0=(m+1)/2 is the critical global existence exponent for the cases Ω=RN∖B1‾ (N≥2) and Ω=B1:={x∈RN:|x|<1} (N≥1).
KW - Blow-up
KW - Critical exponents
KW - Fast diffusion equation
KW - Nonlinear boundary condition
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U2 - 10.1016/j.jmaa.2019.123526
DO - 10.1016/j.jmaa.2019.123526
M3 - Article
AN - SCOPUS:85072734290
VL - 482
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
SN - 0022-247X
IS - 1
M1 - 123526
ER -