On growth and instability for semilinear evolution equations: an abstract approach
DOI10.1007/S00208-023-02733-4zbMATH Open1544.35051MaRDI QIDQ6583563
V. Müller, Yuri Tomilov, Roland Schnaubelt
Publication date: 6 August 2024
Published in: Mathematische Annalen (Search for Journal in Brave)
Asymptotic behavior of solutions to PDEs (35B40) One-parameter semigroups and linear evolution equations (47D06) Stability problems for infinite-dimensional dissipative dynamical systems (37L15) Nonlinear evolution equations (47J35) Measures of noncompactness and condensing mappings, (K)-set contractions, etc. (47H08) Second-order semilinear hyperbolic equations (35L71)
Cites Work
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Stabilization for the semilinear wave equation with geometric control condition
- Eigenmodes of the damped wave equation and small hyperbolic subsets
- Energy decay for the damped wave equation under a pressure condition
- Stability results for the wave equation with indefinite damping
- Differential equations with absolutely unstable trivial solutions
- \(L^{p}\)-Tauberian theorems and \(L^{p}\)-rates for energy decay
- The resolvent growth assumption for semigroups on Hilbert spaces
- Stability theory of solitary waves in the presence of symmetry. II
- Semigroups of linear operators and applications to partial differential equations
- Global instability and essential spectrum in semilinear evolution equations
- Instability of differential equations with respect to the first approximation
- Compact sets in the space \(L^ p(0,T;B)\)
- Stability theory of solitary waves in the presence of symmetry. I
- Feedback stabilization of a linear control system in Hilbert space with an a priori bounded control
- Geometric theory of semilinear parabolic equations
- Classes of linear operators. Vol. I
- Dynamics in one dimension
- The adjoint of a semigroup of linear operators
- Problem of instability in the first approximation
- Multivalued perturbations of \(m\)-accretive differential inclusions
- On the exponential stability of \(C_0\)-semigroups on Banach spaces with compact perturbations
- One-dimensional perturbations of the shift
- Growth bounds of solutions of abstract nonlinear differential equations
- Infinite-dimensional dynamical systems in mechanics and physics.
- Global attractors for damped semilinear wave equations.
- On nonlinear stabilization of linearly unstable maps
- On the bounded compact approximation property and measures of noncompactness
- The asymptotic behaviour of semigroups of linear operators
- An example on Lyapunov stability and linearization
- Imperfect geometric control and overdamping for the damped wave equation
- Linearized stability in the context of an example by Rodrigues and Solà-Morales
- Decay of semilinear damped wave equations: cases without geometric control condition
- Damped wave equations on compact hyperbolic surfaces
- On shadowing and hyperbolicity for geodesic flows on surfaces
- Exponential stabilization without geometric control
- Strong stability of elastic control systems with dissipative saturating feedback
- Sharp polynomial decay rates for the damped wave equation on the torus
- Non-linear semi-groups
- Spectral mapping theorems for essential spectra
- One dimensional perturbations of restricted shifts
- Essentially unstable solutions of finite-difference equations in a Banach space
- Uniform observability estimates for linear waves
- A hypercyclic rank one perturbation of a unitary operator
- Evolution Generated by Semilinear Dissipative Plus Compact Operators
- Linearized instability for nonlinear schrödinger and klein-gordon equations
- Lack of Uniform Stabilization for Noncontractive Semigroups Under Compact Perturbation
- Measures of noncompactness for elements of C^*-algebras
- Essential Spectra of Elementary Operators
- Sharp Sufficient Conditions for the Observation, Control, and Stabilization of Waves from the Boundary
- One-Parameter Semigroups for Linear Evolution Equations
- The rate at which energy decays in a damped String
- Hypercyclic and chaotic semigroups of linear operators
- The Spectrum of the Damped Wave Operator for a Bounded Domain inR2
- Triangular Truncation and Normal Limits of Nilpotent Operators
- Elliptic Carleman Estimates and Applications to Stabilization and Controllability, Volume I
- On hypercyclic rank one perturbations of unitary operators
- Control of eigenfunctions on surfaces of variable curvature
- Spectral theory of linear operators and spectral systems in Banach algebras
- Asymptotic distribution of eigenfrequencies for damped wave equations
- Nonuniform stability of damped contraction semigroups
This page was built for publication: On growth and instability for semilinear evolution equations: an abstract approach
Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6583563)