\(\nu \)-loss of derivatives for an evolution type model

DOI10.1016/J.NA.2009.04.027zbMath1181.35030OpenAlexW2011110020MaRDI QIDQ732571

Xiaojun Lu, Michael Reissig, Daoyuan Fang

Publication date: 9 October 2009

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2009.04.027

zbMATH Keywords

Floquet theoryinstability argument\(p\)-evolution modelprinciple symbols

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Asymptotic behavior of solutions to PDEs (35B40) Initial value problems for second-order hyperbolic equations (35L15) Degenerate hyperbolic equations (35L80) Initial value problems for PDEs with pseudodifferential operators (35S10)

Related Items (5)

On the fractional order hyperbolic equation with random coefficients ⋮ On the optimal regularity of plate equations with randomized time‐dependent coefficients ⋮ On the magnetic Schrödinger hyperbolic equation with randomized coefficients ⋮ On the plate equation with nonstationary stochastic process coefficients ⋮ Counter-examples of regularity behavior for \(\sigma \)-evolution equations

Cites Work

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• \(L^p\)-\(L^q\) estimate for wave equation with bounded time dependent coefficient
• Modulus of continuity of the coefficients and loss of derivatives in the strictly hyperbolic Cauchy problem
• Loss of regularity for \(p\)-evolution type models
• The Log-effect for \(p\)-evolution type models
• Partial differential equations. 2: Qualitative studies of linear equations
• Loss of derivatives in evolution Cauchy problems
• Does the loss of regularity really appear?
• One application of Floquet's theory toLp-Lq estimates for hyperbolic equations with very fast oscillations

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