Dissipativity in the sense of Levinson for a class of second—order nonlinear evolution equations

DOI10.1016/0362-546X(82)90031-1zbMath0505.35012OpenAlexW2093882611MaRDI QIDQ4740875

Alain Haraux

Publication date: 1982

Published in: Nonlinear Analysis: Theory, Methods & Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0362-546x(82)90031-1

zbMATH Keywords

existenceregular boundarycompactness of trajectoriesLevinson dissipativityhyperbolic equations with dissipationsecond-order nonlinear evolution equations

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) Periodic solutions to PDEs (35B10) Nonlinear differential equations in abstract spaces (34G20) Second-order nonlinear hyperbolic equations (35L70) A priori estimates in context of PDEs (35B45)

Related Items (10)

A sharp ultimate bound of the solutions to some second-order evolution equations with nonlinear damping ⋮ Density of the range of a wave operator with nonmonotone superlinear nonlinearity ⋮ Asymptotic stability of solutions to the Navier–Stokes–Fourier system driven by inhomogeneous Dirichlet boundary conditions ⋮ Dynamic von Kármán equations involving nonlinear damping: Time-periodic solutions ⋮ Almost periodic solutions for a semilinear quasi-autonomous hyperbolic problem ⋮ New results in the theory of multivalued mappings. I: Topological characteristics and solvability of operator relations ⋮ On the ultimate energy bound of solutions to some forced second-order evolution equations with a general nonlinear damping operator ⋮ Attractors of asymptotically compact processes and applications to nonlinear partial differential equations ⋮ Anti-periodic solutions of some nonlinear evolution equations ⋮ Non-resonance for a strongly dissipative wave equation in higher dimensions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Asymptotic behavior for an almost periodic, strongly dissipative wave equation
• Bounded or almost periodic solution of the non linear vibrating membrane equation
• Soluzioni periodiche dell'equazione delle onde con termine dissipativo non lineare
• On continuity of functions with values in various Banach spaces
• Solutions faibles d'équations d'évolution dans les espaces de Hilbert. (Weak solution of evolution equations in Hilbert spaces)
• Problèmes unilateraux
• Initial value problems and time-periodic solutions for a nonlinear wave equation
• Almost-periodic forcing for a wave equation with a nonlinear, local damping term
• Forced vibrations for a nonlinear wave equation
• Some non-linear evolution equations

This page was built for publication: Dissipativity in the sense of Levinson for a class of second—order nonlinear evolution equations