A weighted sobolev space theory for the diffusion-wave equations with time-fractional derivatives on C1 domains

Beom Seok Han, Kyeong Hun Kim, Daehan Park

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)3415-3445
Number of pages31
JournalDiscrete and Continuous Dynamical Systems- Series A
Volume41
Issue number7
DOIs
Publication statusPublished - 2021 Jul

Keywords

  • Caputo fractional derivative
  • Domains domains
  • Sobolev space with weights
  • Time-fractional equation
  • Variable coefficients

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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