\(L^1-L^1\) estimates for a doubly dissipative semilinear wave equation

DOI10.1007/s00030-016-0428-4zbMath1367.35092OpenAlexW2562447555MaRDI QIDQ523546

Marcello D'Abbicco

Publication date: 21 April 2017

Published in: NoDEA. Nonlinear Differential Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00030-016-0428-4

zbMATH Keywords

frictionpower nonlinearitydecay estimatesGagliardo-Nirenberg inequalityglobal small data solutionsvisco-elastic damping

Mathematics Subject Classification ID

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 (13)

A general nonexistence result for inhomogeneous semilinear wave equations with double damping and potential terms ⋮ Regular attractor of the β-evolution equation with fractional damping on Rn ⋮ Semilinear \(\sigma\)-evolution models with friction and visco-elastic type damping ⋮ Decay estimates for the double dispersion equation with initial data in real Hardy spaces ⋮ On asymptotic properties of solutions to \(\sigma \)-evolution equations with general double damping ⋮ Dissipative higher order hyperbolic equations ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Long Time Decay Estimates in Real Hardy Spaces for the Double Dispersion Equation ⋮ Study of semi-linear \(\sigma\)-evolution equations with frictional and visco-elastic damping ⋮ \(L^1-L^1\) estimates for the strongly damped plate equation ⋮ Dissipative structure and diffusion phenomena for doubly dissipative elastic waves in two space dimensions ⋮ Global small data solutions for semilinear waves with two dissipative terms

Cites Work

• Unnamed Item
• A new phenomenon in the critical exponent for structurally damped semi-linear evolution equations
• Convergence to nonlinear diffusion waves for solutions of a system of hyperbolic conservation laws with damping
• On the asymptotic behavior of solutions of semi-linear wave equations
• The \(L^{p}\)--\(L^{q}\) estimates of solutions to one-dimensional damped wave equations and their application to the compressible flow through porous media
• \(L^p\)-\(L^q\) estimates of solutions to the damped wave equation in 3-dimensional space and their application
• Nonlinear Liouville theorems for Grushin and Tricomi operators.
• Decay estimates of solutions for dissipative wave equations in \(\mathbb R^N\) with lower power nonlinearities
• \(L^p\)-\(L^q\) estimates for damped wave equations and their applications to semi-linear problem
• An application of \(L^p-L^q\) decay estimates to the semi-linear wave equation with parabolic-like structural damping
• A blow-up result for a nonlinear wave equation with damping: The critical case
• Asymptotic profile of solutions for wave equations with frictional and viscoelastic damping terms
• L 1 Estimates for Oscillating Integrals Related to Structural Damped Wave Models
• Semilinear structural damped waves
• A Benefit from the L ∞ Smallness of Initial Data for the Semilinear Wave Equation with Structural Damping
• On the diffusion phenomenon of quasilinear hyperbolic waves
• Critical exponent for a nonlinear wave equation with damping

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