Existence, uniqueness and asymptotic behavior for solutions of the nonlinear beam equation

DOI10.1016/0362-546X(90)90041-EzbMath0704.45013MaRDI QIDQ3483827

Ducival Carvalho Pereira

Publication date: 1990

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

zbMATH Keywords

existenceasymptotic behavioruniquenessHilbert spaceinitial value problemnonlinear beam equationsecond-order equationlinear unbounded operator

Mathematics Subject Classification ID

Integro-partial differential equations (45K05) Nonlinear differential equations in abstract spaces (34G20) Second-order nonlinear hyperbolic equations (35L70) Abstract integral equations, integral equations in abstract spaces (45N05)

Related Items (23)

Variational inequality for a nonlinear model of the oscillations of beams ⋮ Existence, uniqueness and uniform decay for the nonlinear beam degenerate equation with weak damping ⋮ On a nonlinear degenerate evolution equation with nonlinear boundary damping ⋮ A Galerkin–Newton Algorithm for Solution of a Kirchhoff-Type Static Equation ⋮ Regular solutions of a nonlinear model for vibrations of beams in unbounded domains ⋮ Existence of solutions to strongly damped plate or beam equations ⋮ Optimal control problem for a viscoelastic beam and its Galerkin approximation ⋮ Remarks on thin quasilinear plates with mixed boundary conditions ⋮ Global attractor and inertial set for the beam equation ⋮ Existence of solutions of nonlinear extensible beam equations ⋮ Beam equation with weak-internal damping in domain with moving boundary. ⋮ Exponential decay to the degenerate nonlinear coupled beams system with weak damping ⋮ On nonlinear hyperbolic equation in unbounded domain ⋮ Energy decay for the strongly damped nonlinear beam equation and its applications in moving boundary ⋮ Beam evolution equation with variable coefficients ⋮ On the vibrations of a simply supported square plate on a weakly nonlinear elastic foundation ⋮ Remarks on the beam evolution equations in noncylindrical domains ⋮ Pareto optimal control problem and its Galerkin approximation for a nonlinear one-dimensional extensible beam equation ⋮ Numerical solution of the static beam problem by Bernoulli collocation method ⋮ On the solutions for an extensible beam equation with internal damping and source terms ⋮ A numerical algorithm for a Kirchhoff-type nonlinear static beam ⋮ Unnamed Item ⋮ Similarity reductions of a nonlinear model for vibrations of beams

Cites Work

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• On a new class of nonlinear wave equations
• Nonlinear vibration of beams and rectangular plates
• Free vibrations and dynamic buckling of the extensible beam
• Stability theory for an extensible beam
• Initial-boundary value problems for an extensible beam
• Decay estimates for the generalized damped extensible string and beam equations
• Remark on the decay for damped string and beam equations
• Nonlinear initial-boundary value problems
• On global classical solutions of a nonlinear wave equation

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