Bounded solutions of second order semilinear evolution equations and applications to the telegraph equation

DOI10.1016/S0021-7824(99)80009-9zbMath0927.34048OpenAlexW2083101896MaRDI QIDQ1282445

Rafael Ortega, Jose Miguel-Alonso, Jean Mawhin

Publication date: 13 December 1999

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0021-7824(99)80009-9

zbMATH Keywords

bounded solutionsnonlinear telegraph equationsabstract semilinear evolution equations

Mathematics Subject Classification ID

Initial-boundary value problems for second-order hyperbolic equations (35L20) Nonlinear differential equations in abstract spaces (34G20) Second-order nonlinear hyperbolic equations (35L70) Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators (34L20)

Related Items (14)

A numerical method for solving the hyperbolic telegraph equation ⋮ Existence, stability and smoothness of a bounded solution for nonlinear time-varying thermoelastic plate equations ⋮ Solution of the second-order one-dimensional hyperbolic telegraph equation by using the dual reciprocity boundary integral equation (DRBIE) method ⋮ Fredholm solvability of a periodic Neumann problem for a linear telegraph equation ⋮ Scorza-Dragoni approach to Dirichlet problem in Banach spaces ⋮ Sharp estimates of bounded solutions to some second-order forced dissipative equations ⋮ Legendre multiwavelet Galerkin method for solving the hyperbolic telegraph equation ⋮ Parallel implementation of 2-D telegraphic equation on MPI/PVM cluster ⋮ A duality theorem for periodic solutions of a class of second order evolution equations ⋮ Application of polynomial scaling functions for numerical solution of telegraph equation ⋮ Asymptotic boundary value problems for second-order differential systems ⋮ Transparent boundary conditions and numerical computation for singularly perturbed telegraph equation on unbounded domain ⋮ Exact controllability of the suspension bridge model proposed by Lazer and McKenna ⋮ A maximum principle for bounded solutions of the telegraph equations and applications to nonlinear forcings

Cites Work

• Attractors for damped nonlinear hyperbolic equations
• Infinite-dimensional dynamical systems in mechanics and physics
• Bounded, periodic or almost-periodic solutions of nonlinear hyperbolic partial differential equations
• A boundedness result of Landesman-Lazer type
• An iterative scheme for the \(N\)-competing species problem
• Bounded solutions of nonlinear second order ordinary differential equations
• Global asymptotic stability of a forced Newtonian system with dissipation
• Almost periodic properties of ordinary differential equations
• Generalized periodic solutions of nonlinear telegraph equations
• Bounded Solutions of Some Second Order Nonlinear Differential Equations
• Resonance and non-resonance in a problem of boundedness
• A Nonstandard Resonance Problem for Ordinary Differential Equations
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