Stabilization of hyperbolic and parabolic systems with nonlinearly perturbed boundary conditions

DOI10.1016/0022-0396(88)90129-5zbMath0665.35011OpenAlexW2107288043MaRDI QIDQ1116012

Irena Lasiecka

Publication date: 1988

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

Full work available at URL: https://doi.org/10.1016/0022-0396(88)90129-5

zbMATH Keywords

wave equationanalytic semigroupsabstract systemsnonlinear perturbationprinciple of linearized stabilityunbounded perturbationsDirichlet or Neumann conditionfeedback operatorlocal exponential stabilizability

Mathematics Subject Classification ID

Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations (35K60) Stability in context of PDEs (35B35) Nonlinear differential equations in abstract spaces (34G20) Second-order nonlinear hyperbolic equations (35L70)

Related Items (14)

Blow-up for the wave equation with nonlinear source and boundary damping terms ⋮ Exponential stabilization of hyperbolic systems with nonlinear, unbounded perturbations—riccati operator approach ⋮ Well-posedness and optimal decay rates for the wave equation with nonlinear boundary damping-source interaction ⋮ On the wave equation with semilinear porous acoustic boundary conditions ⋮ Uniform stabilization of a nonlinearly perturbed Kirchhoff plate ⋮ Galerkin approximations of infinite-dimensional compensators for flexible structures with unbounded control action ⋮ Strong stability and uniform decay of solutions to a wave equation with semilinear porous acoustic boundary conditions ⋮ On invariance of \(p\)-admissibility of control and observation operators to \(q\)-type of perturbations of generator of \(C_{0}\)-semigroup ⋮ Global existence and uniform decay for wave equation with dissipative term and boundary damping ⋮ Stabilization of parabolic systems via a degenerate nonnegative feedback ⋮ Global uniform decay rates for the solutions to wave equation with nonlinear boundary conditions ⋮ Global existence and uniform stabilization of a generalized dissipative Klein–Gordon equation type with boundary damping ⋮ Stabilization of the semilinear wave equation with viscous damping ⋮ Numerical approximations and regularizations of Riccati equations arising in hyperbolic dynamics with unbounded control operators

Cites Work

• Stabilization of Neumann boundary feedback of parabolic equations: The case of trace in the feedback loop
• Regularity of hyperbolic equations under \(L^ 2(0,T;L_ 2(\Gamma))\)- Dirichlet boundary terms
• Decay of solutions of wave equations in a bounded region with boundary dissipation
• Uniform exponential energy decay of wave equations in a bounded region with \(L_ 2(0,\infty;L_ 2(\Gamma))\)-feedback control in the Dirichlet boundary conditions
• Non homogeneous boundary value problems for second order hyperbolic operators
• Boundary feedback stabilizability of parabolic equations
• Decay rates for weakly damped systems in Hilbert space obtained with control-theoretic methods
• Stability and semilinear evolution equations in Hilbert space
• Stabilization and Structural Assignment of Dirichlet Boundary Feedback Parabolic Equations
• A Note on Stabilization of Infinite Dimensional Linear Oscillators by Compact Linear Feedback
• A Note on the Boundary Stabilization of the Wave Equation
• A Note on Weak Stabilizability of Contraction Semigroups
• Concrete characterization of the domains of fractional powers of some elliptic differential operators of the second order
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