Remarks on the Asymptotic Behavior of Solutions to Damped Evolution Equations in Hilbert Space
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Publication:4199275
DOI10.2307/2042664zbMath0411.47010OpenAlexW4253978491MaRDI QIDQ4199275
Publication date: 1979
Full work available at URL: https://doi.org/10.2307/2042664
asymptotic stabilityasymptotic behavior of solutionsdamped evolution equationdecays at a uniform exponential rate
Asymptotic behavior of solutions to PDEs (35B40) Equations and inequalities involving linear operators, with vector unknowns (47A50)
Related Items (3)
Asymptotic bounds for solutions to a system of damped integrodifferential equations of electromagnetic theory ⋮ On exponential growth estimates for solutions of ill-posed integrodifferential initial-history value problems ⋮ Asymptotic behavior of solutions to the damped quasilinear equation \(\partial^ 2/\partial t^ 2 u(x,t) + \gamma \partial u/\partial t (x,t) - \partial/\partial x \sigma(\partial u/\partial t)\)
Cites Work
- Uniqueness and growth of weak solutions to certain linear differential equations in Hilbert space
- Decay rates for weakly damped systems in Hilbert space obtained with control-theoretic methods
- Some nonexistence and instability theorems for solutions of formally parabolic equations of the form \(Pu_t=-Au+ {\mathfrak F} (u)\)
- Nonexistence theorems for the heat equation with nonlinear boundary conditions and for the porous medium equation backward in time
- Logarithmic convexity and the Cauchy problem for some abstract second order differential inequalities
- Growth estimates for solutions of evolutionary equations in Hilbert space with applications in elastodynamics
- Some Nonexistence Theorem for Initial-Boundary Value Problems with Nonlinear Boundary Constraints
- Instability and Nonexistence of Global Solutions to Nonlinear Wave Equations of the Form Pu tt = -Au + ℱ(u)
- Logarithmic Convexity, First Order Differential Inequalities and Some Applications
- Wave Equations with Weak Damping
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