Decay estimates for the generalized damped extensible string and beam equations

DOI10.1016/0362-546X(84)90059-2zbMath0524.35026MaRDI QIDQ3037886

Eliana Henriques De Brito

Publication date: 1984

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

zbMATH Keywords

initial-boundary value problemsCauchy problemsdecay estimatesdamped extensible string and beam equation

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Asymptotic behavior of solutions to PDEs (35B40) Nonlinear differential equations in abstract spaces (34G20) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Initial value problems for nonlinear higher-order PDEs (35G25)

Related Items

Global existence and asymptotic behavior for a mildly degenerate Kirchhoff wave equation with boundary damping ⋮ Existence, uniqueness and uniform decay for the nonlinear beam degenerate equation with weak damping ⋮ Parameter identification problems for an extensible beam equation ⋮ A Galerkin–Newton Algorithm for Solution of a Kirchhoff-Type Static Equation ⋮ On a global solution and asymptotic behaviour for the generalized damped extensible beam equation ⋮ Energy decay of solutions for an extensible beam equation with a weak nonlinear dissipation ⋮ Energy decay for a viscoelastic Kirchhoff plate equation with a delay term ⋮ Global solutions for dissipative Kirchhoff strings with non-Lipschitz nonlinear term ⋮ Global existence and blow-up of solutions for a Kirchhoff type plate equation with damping ⋮ Global well-posedness and stability for a viscoelastic plate equation with a time delay ⋮ Existence, uniqueness and asymptotic behavior for solutions of the nonlinear beam equation ⋮ Remark on the decay for damped string and beam equations ⋮ Nonlinear initial-boundary value problems ⋮ Low regularity global solutions for nonlinear evolution equations of Kirchhoff type ⋮ Remarks on thin quasilinear plates with mixed boundary conditions ⋮ Fréchet differentiability for an extensible beam equation and its application to bilinear minimax control problems ⋮ Global existence of solutions and energy decay for a Kirchhoff-type equation with nonlinear dissipation ⋮ Minimax optimal control problems for an extensible beam equation with uncertain initial velocity ⋮ Stability of strong attractors for the extensible beam equation with gentle dissipation ⋮ Existence of solutions of nonlinear extensible beam equations ⋮ Beam equation with weak-internal damping in domain with moving boundary. ⋮ Convergence of a semi-discrete scheme for an abstract nonlinear second order evolution equation ⋮ Hyperbolic-parabolic singular perturbation for mildly degenerate Kirchhoff equations: Time-decay estimates ⋮ Beam evolution equation with variable coefficients ⋮ GLOBAL EXISTENCE AND ASYMPTOTIC STABILITY FOR THE NONLINEAR AND GENERALIZED DAMPED EXTENSIBLE PLATE EQUATION ⋮ Global solution and asymptotic behavior for the variable coefficient beam equation with nonlinear damping ⋮ Decay estimates for the Cauchy problem for the damped extensible beam equation ⋮ Remarks on the beam evolution equations in noncylindrical domains ⋮ On the solutions for an extensible beam equation with internal damping and source terms ⋮ Optimal control problems for an extensible beam equation ⋮ Global attractor for an extensible beam equation with localized nonlinear damping and linear memory ⋮ Uniform attractors for a nonautonomous extensible plate equation with a strong damping ⋮ A numerical algorithm for a Kirchhoff-type nonlinear static beam ⋮ Global well-posedness analysis for the nonlinear extensible beam equations in a class of modified Woinowsky-Krieger models ⋮ Global existence and general decay for a nonlinear viscoelastic equation with nonlinear localized damping and velocity-dependent material density ⋮ On stability and convergence of a three-layer semi-discrete scheme for an abstract analogue of the Ball integro-differential equation ⋮ Unnamed Item ⋮ Some remarks on global solutions to nonlinear dissipative mildly degenerate Kirchhoff strings ⋮ Finite-dimensional attractors for a general class of nonautonomous wave equations ⋮ Optimal control problems for an extensible beam equation with pointwise state constraints ⋮ General decay for a nonlinear beam equation with weak dissipation ⋮ Global solutions for dissipative Kirchhoff strings with \(m(r)=r^p\) \((p<1)\) ⋮ Decay rate estimates for a weak viscoelastic beam equation with time-varying delay

Cites Work

• A non-linear hyperbolic equation
• Dynamic Stability of Equilibrium States of the Extensible Beam
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item