TY - JOUR
T1 - A weighted sobolev space theory for the diffusion-wave equations with time-fractional derivatives on C1 domains
AU - Han, Beom Seok
AU - Kim, Kyeong Hun
AU - Park, Daehan
N1 - Funding Information:
2020 Mathematics Subject Classification. 45D05, 45K05, 45N05, 35B65, 26A33. Key words and phrases. Time-fractional equation, Caputo fractional derivative, Sobolev space with weights, variable coefficients, C1 domains. The authors were supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (No. NRF-2019R1A5A1028324). ∗ Corresponding author.
Publisher Copyright:
© 2021 American Institute of Mathematical Sciences. All rights reserved.
PY - 2021/7
Y1 - 2021/7
N2 - We introduce a weighted Lp-theory (p > 1) for the time-fractional diffusion-wave equation of the type ∂tαu(t, x) = aij(t, x)uxixj (t, x) + f(t, x), t > 0, x ∈ Ω, where α ∈ (0, 2), ∂tα denotes the Caputo fractional derivative of order α, and Ω is a C1 domain in Rd. We prove existence and uniqueness results in Sobolev spaces with weights which allow derivatives of solutions to blow up near the boundary. The order of derivatives of solutions can be any real number, and in particular it can be fractional or negative.
AB - We introduce a weighted Lp-theory (p > 1) for the time-fractional diffusion-wave equation of the type ∂tαu(t, x) = aij(t, x)uxixj (t, x) + f(t, x), t > 0, x ∈ Ω, where α ∈ (0, 2), ∂tα denotes the Caputo fractional derivative of order α, and Ω is a C1 domain in Rd. We prove existence and uniqueness results in Sobolev spaces with weights which allow derivatives of solutions to blow up near the boundary. The order of derivatives of solutions can be any real number, and in particular it can be fractional or negative.
KW - Caputo fractional derivative
KW - Domains domains
KW - Sobolev space with weights
KW - Time-fractional equation
KW - Variable coefficients
UR - http://www.scopus.com/inward/record.url?scp=85103787926&partnerID=8YFLogxK
U2 - 10.3934/dcds.2021002
DO - 10.3934/dcds.2021002
M3 - Article
AN - SCOPUS:85103787926
SN - 1078-0947
VL - 41
SP - 3415
EP - 3445
JO - Discrete and Continuous Dynamical Systems- Series A
JF - Discrete and Continuous Dynamical Systems- Series A
IS - 7
ER -