Weighted \(L_q(L_{p})\)-estimate with Muckenhoupt weights for the diffusion-wave equations with time-fractional derivatives

DOI10.1016/J.JDE.2020.03.005zbMath1448.35545arXiv1911.07437OpenAlexW3011415850MaRDI QIDQ2180588

Daehan Park, Beom-Seok Han, Kyeong-Hun Kim

Publication date: 14 May 2020

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1911.07437

zbMATH Keywords

Caputo fractional derivativeMuckenhoupt \(A_p\) weights\( L_q( L_p)\)-theory

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Integro-partial differential equations (45K05) Fractional derivatives and integrals (26A33) Initial value problems for second-order parabolic equations (35K15) Volterra integral equations (45D05) Abstract integral equations, integral equations in abstract spaces (45N05) Fractional partial differential equations (35R11)

Related Items (10)

Weighted mixed norm estimates for fractional wave equations with VMO coefficients ⋮ Weighted maximal \(L_q (L_p)\)-regularity theory for time-fractional diffusion-wave equations with variable coefficients ⋮ A weighted \(L_p\)-regularity theory for parabolic partial differential equations with time-measurable pseudo-differential operators ⋮ Global existence and convergence results for a class of nonlinear time fractional diffusion equation ⋮ New notion of mild solutions for higher-order Riemann-Liouville fractional systems involving non-instantaneous impulses ⋮ Sobolev estimates for fractional parabolic equations with space-time non-local operators ⋮ Stability and asymptotics for fractional delay diffusion‐wave equations ⋮ Local/global existence analysis of fractional wave equations with exponential nonlinearity ⋮ An approach for weighted mixed-norm estimates for parabolic equations with local and non-local time derivatives ⋮ A weighted Sobolev space theory for the diffusion-wave equations with time-fractional derivatives on \(C^1\) domains

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