A WEIGHTED SOBOLEV SPACE THEORY FOR THE DIFFUSION-WAVE EQUATIONS WITH TIME-FRACTIONAL DERIVATIVES ON C( )(1)DOMAINS
- Authors
- Han, Beom-Seok; Kim, Kyeong-Hun; Park, Daehan
- Issue Date
- 7월-2021
- Publisher
- AMER INST MATHEMATICAL SCIENCES-AIMS
- Keywords
- Time-fractional equation; Caputo fractional derivative; Sobolev space with weights; variable coefficients; C-1 domains
- Citation
- DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, v.41, no.7, pp.3415 - 3445
- Indexed
- SCIE
SCOPUS
- Journal Title
- DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
- Volume
- 41
- Number
- 7
- Start Page
- 3415
- End Page
- 3445
- URI
- https://scholar.korea.ac.kr/handle/2021.sw.korea/127787
- DOI
- 10.3934/dcds.2021002
- ISSN
- 1078-0947
- Abstract
- We introduce a weighted L-p-theory (p > 1) for the time-fractional diffusion-wave equation of the type partial derivative(alpha )(t)u(t, x) = a(ij) (t, x)u(x)i(x)j (t, x) f (t, x), t > 0, x is an element of Omega, where alpha is an element of (0,2), partial derivative(alpha)(t) denotes the Caputo fractional derivative of order alpha, and Omega is a C-1 domain in R-d. 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.
- Files in This Item
- There are no files associated with this item.
- Appears in
Collections - College of Science > Department of Mathematics > 1. Journal Articles
Items in ScholarWorks are protected by copyright, with all rights reserved, unless otherwise indicated.