Semilinear \(p\)-evolution equations in Sobolev spaces

DOI10.1016/j.jde.2016.01.035zbMath1336.35117arXiv1508.00020OpenAlexW2264768973MaRDI QIDQ264480

Chiara Boiti, Alessia Ascanelli

Publication date: 31 March 2016

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

Full work available at URL: https://arxiv.org/abs/1508.00020

zbMATH Keywords

time-dependent coefficientsdiagonalization procedurelocal in time well-posednessNash-Moser theoremwell-posedness in Sobolev spaces\(H^\infty\) well-posednessloss of regularityfactorization procedure

Mathematics Subject Classification ID

Initial value problems for nonlinear higher-order PDEs (35G25) Initial value problems for linear higher-order PDEs (35G10) Initial value problems for PDEs with pseudodifferential operators (35S10) Graded Fréchet spaces and tame operators (46A61)

Related Items (9)

Semilinear \(p\)-evolution equations in Sobolev spaces ⋮ The Cauchy problem for 3-evolution equations with data in Gelfand-Shilov spaces ⋮ Random-field solutions to linear hyperbolic stochastic partial differential equations with variable coefficients ⋮ Well-posedness of the Cauchy problem for \(p\)-evolution systems of pseudo-differential operators ⋮ Semilinear \(p\)-evolution equations in weighted Sobolev spaces ⋮ KdV-type equations in projective Gevrey spaces ⋮ Well-posedness in Sobolev spaces for semi-linear 3-evolution equations ⋮ Weighted energy estimates for \(p\)-evolution equations in \textit{SG} classes ⋮ Schrödinger-type equations in Gelfand-Shilov spaces

Cites Work

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• Local existence for semilinear weakly hyperbolic equations with time dependent coefficients
• The Cauchy problem for 𝑝-evolution equations
• Schrödinger equations of higher order
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