A note on \(L^p - L^q\) estimates for semilinear critical dissipative Klein-Gordon equations

DOI10.1007/S10884-019-09818-2zbMath1465.35296OpenAlexW2995747491MaRDI QIDQ2225490

Alessandro Palmieri, Marcello D'Abbicco

Publication date: 8 February 2021

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

Full work available at URL: https://doi.org/10.1007/s10884-019-09818-2

zbMATH Keywords

semilinear wave equationpower nonlinearityscale-invariant dissipationscale-invariant masssmall data energy solutions

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Critical exponents in context of PDEs (35B33) A priori estimates in context of PDEs (35B45) Initial value problems for second-order hyperbolic equations (35L15) Second-order semilinear hyperbolic equations (35L71)

Related Items (4)

A blow-up result for a semilinear wave equation with scale-invariant damping and mass and nonlinearity of derivative type ⋮ Weakly coupled system of semilinear wave equations with distinct scale-invariant terms in the linear part ⋮ Small data solutions for the Euler-Poisson-Darboux equation with a power nonlinearity ⋮ The Cauchy problem for the nonlinear viscous Boussinesq equation in the \(L^q\) framework

Cites Work

• NLWE with a special scale invariant damping in odd space dimension
• Semi-linear wave equations with effective damping
• Fourier analysis. Pseudo-differential operators, time-frequency analysis and partial differential equation. Based on the presentations at the international conference, Aalto University, near Helsinki, Finland, June 25--29, 2012
• A scale-invariant Klein-Gordon model with time-dependent potential
• A shift in the strauss exponent for semilinear wave equations with a not effective damping
• Nonlinear scattering theory at low energy
• On the asymptotic behavior of solutions of semi-linear wave equations
• A competition between Fujita and Strauss type exponents for blow-up of semi-linear wave equations with scale-invariant damping and mass
• Life-span of solutions to semilinear wave equation with time-dependent critical damping for specially localized initial data
• A scale of critical exponents for semilinear waves with time-dependent damping and mass terms
• Global existence of solutions for semi-linear wave equation with scale-invariant damping and mass in exponentially weighted spaces
• Critical exponent for the semilinear wave equation with time-dependent damping
• Blow-up for semilinear wave equations with the scale invariant damping and super-Fujita exponent
• Lifespan of semilinear wave equation with scale invariant dissipation and mass and sub-Strauss power nonlinearity
• Semilinear damped Klein-Gordon models with time-dependent coefficients
• Global existence results for a semilinear wave equation with scale-invariant damping and mass in odd space dimension
• A blow-up result for a nonlinear wave equation with damping: The critical case
• Semi‐linear wave models with power non‐linearity and scale‐invariant time‐dependent mass and dissipation, II
• The threshold of effective damping for semilinear wave equations
• Semi‐linear wave models with power non‐linearity and scale‐invariant time‐dependent mass and dissipation
• A global existence result for a semilinear scale‐invariant wave equation in even dimension
• Critical exponent for a nonlinear wave equation with damping

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