Long-time behavior and convergence for semilinear wave equations on \(\mathbb{R}^ N\)

DOI10.1007/BF02219055zbMath0879.35109OpenAlexW1990352380MaRDI QIDQ1363326

Eduard Feireisl

Publication date: 18 January 1998

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

Full work available at URL: https://doi.org/10.1007/bf02219055

zbMATH Keywords

small initial energyground-state solutionconcentrated compactness

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Second-order nonlinear hyperbolic equations (35L70) Initial value problems for second-order hyperbolic equations (35L15)

Related Items (9)

Attractors and approximations for lattice dynamical systems ⋮ Symmetry Properties of Positive Solutions of Parabolic Equations on ℝ^N: I. Asymptotic Symmetry for the Cauchy Problem ⋮ Decay rate of solutions to hyperbolic system of first order ⋮ APPLICATIONS OF THE ŁOJASIEWICZ–SIMON, GRADIENT INEQUALITY TO GRADIENT-LIKE EVOLUTION EQUATIONS ⋮ Attractor for lattice system of dissipative Zakharov equation ⋮ Spatially extended differential equations in a potential: On the borders of the basins of attraction related to local minima ⋮ Symmetry Properties of Positive Solutions of Parabolic Equations on ℝ^N: II. Entire Solutions ⋮ Long-time asymptotic expansion for the damped semilinear wave equation. ⋮ Attractors for second order lattice dynamical systems

Cites Work

• Nonlinear scalar field equations. I: Existence of a ground state
• The concentration-compactness principle in the calculus of variations. The locally compact case. I
• Semigroups of linear operators and applications to partial differential equations
• Convergence in gradient-like systems with applications to PDE
• Infinite-dimensional dynamical systems in mechanics and physics
• Convergence to a ground state as a threshold phenomenon in nonlinear parabolic equations
• Uniqueness of the ground state solutions of △u+f(u)=0 in Rⁿ, n≥3
• On the dynamics of semilinear damped wave equations on
• Instability and Nonexistence of Global Solutions to Nonlinear Wave Equations of the Form Pu tt = -Au + ℱ(u)
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