A scale-invariant Klein-Gordon model with time-dependent potential

DOI10.1007/s11565-012-0153-9zbMath1326.35184OpenAlexW2158752019MaRDI QIDQ473502

Christiane Böhme, Michael Reissig

Publication date: 24 November 2014

Published in: Annali dell'Università di Ferrara. Sezione VII. Scienze Matematiche (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11565-012-0153-9

zbMATH Keywords

Klein-Gordon equationtime-dependent massscale-invariancegeneralized energy conservation\(L^p\)-\(L^q\) decay estimates

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Initial value problems for second-order hyperbolic equations (35L15)

Related Items (15)

On \(t\)-dependent hyperbolic systems. II. ⋮ Energy estimates for the Cauchy problem of Klein-Gordon-type equations with non-effective and very fast oscillating time-dependent potential ⋮ A class of dissipative wave equations with time-dependent speed and damping ⋮ Regularity theory and global existence of small data solutions to semi-linear de Sitter models with power non-linearity ⋮ Semilinear evolution models with scale-invariant friction and visco-elastic damping ⋮ Scale-invariant semilinear damped wave models with mass term and integrable in time speed of propagation. ⋮ Novel symplectic integrators for the Klein-Gordon equation with space- and time-dependent mass ⋮ Classification of asymptotic profiles for the Cauchy problem of damped beam equation with two variable coefficients: effective damping case ⋮ Energy bounds for Klein-Gordon equations with time-dependent potential ⋮ A note on \(L^p - L^q\) estimates for semilinear critical dissipative Klein-Gordon equations ⋮ Scattering and asymptotic order for the wave equations with the scale-invariant damping and mass ⋮ Unnamed Item ⋮ Klein-Gordon equations with homogeneous time-dependent electric fields ⋮ Remarks on asymptotic order for the linear wave equation with the scale-invariant damping and mass with 𝐿^{𝑟}-data ⋮ The threshold of effective damping for semilinear wave equations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Generalized energy conservation for Klein-Gordon type equations
• Dispersive estimates for hyperbolic systems with time-dependent coefficients
• Estimates for translation invariant operators in \(L^p\) spaces
• Wave equations with time-dependent dissipation. I: Non-effective dissipation
• Wave equations with time-dependent dissipation. II: Effective dissipation
• \(L^p\)-Abschätzungen und klassische Lösungen für nichtlineare Wellengleichungen. I
• On \(L_2-L_{p'}\) estimates for the wave-equation
• \(L^ p\)-decay rates for homogeneous wave-equations
• Solution representations for a wave equation with weak dissipation
• Convolutions with Kernels Having Singularities on a Sphere

This page was built for publication: A scale-invariant Klein-Gordon model with time-dependent potential