𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Time decay of solutions of semilinear strongly damped generalized wave equations

✍ Scribed by Piotr Biler

Publisher
John Wiley and Sons
Year
1991
Tongue
English
Weight
917 KB
Volume
14
Category
Article
ISSN
0170-4214

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

We study the asymptotic behaviour in time of the solutions of dissipative perturbations of wave‐type equations in ℝ^N^, u~tt~ + Bu~t~ + Au + G(u) = 0, with commuting positive operators A, B and a power like non‐linearity G(u). First we give some (pseudo) conformal invariants of the linear operator in the equation. This allows us to derive optimal decay rates for the solutions of the linearized problems. We then prove some decay estimates for the non‐linear problems using the tools of scattering theory and the aforementioned conformal invariants.

πŸ“œ SIMILAR VOLUMES

Partition of energy in strongly damped g
Partition of energy in strongly damped generalized wave equations
✍ Piotr Biler πŸ“‚ Article πŸ“… 1990 πŸ› John Wiley and Sons 🌐 English βš– 430 KB

## Abstract Dissipative perturbations of hyperbolic equations such as __u__~__tt__~ + __Bu__~__t__~ + __A__^2^__u__ = 0 with positive operators __A__, __B__ are considered. The rates of decay and partition of energy theorems are established for solutions of these equations.

Time Singular Limit of Semilinear Wave E
Time Singular Limit of Semilinear Wave Equations with Damping
✍ B. Najman πŸ“‚ Article πŸ“… 1993 πŸ› Elsevier Science 🌐 English βš– 617 KB

The hyperbolic semilinear initial value problem \(\varepsilon u_{t}+A u_{1}+B u+f(u)=0\), \(u(0)=u_{0,}, u_{t}(0)=u_{1 s}\), with commuting positive selfadjoint operators \(A\) and \(B\) in a Hilbert space \(X\) is considered. The term \(A u\), is a damping term. It is shown that the solutions conve

Space-time decay for solutions of wave e
Space-time decay for solutions of wave equations
✍ Irving Segal πŸ“‚ Article πŸ“… 1976 πŸ› Elsevier Science 🌐 English βš– 321 KB

## IN MEMORY OF NORMAN LEVINSON The LB norm in space-time of a solution of the Klein-Gordon equation in two space-time dimensions is bounded relative to the Lorentz-invariant Hilbert space norm; the L, norms for p > 6 are bounded relative to certain similar larger Hilbert space norms, including th