✦ LIBER ✦

Exact Controllability for Semilinear Wave Equations

✍ Scribed by Liangyu Li; Xu Zhang

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 81 KB
Volume: 250
Category: Article
ISSN: 0022-247X
DOI: 10.1006/jmaa.2000.6998

No coin nor oath required. For personal study only.

✦ Synopsis

In this note, we prove the exact controllability for the semilinear wave equations in any space dimensions under the condition that the nonlinearity behaves like Ž< < < < .

' o s ln s as s ª ϱ.

📜 SIMILAR VOLUMES

Exact boundary controllability for non-a

Exact boundary controllability for non-autonomous quasilinear wave equations

✍ Zhiqiang Wang 📂 Article 📅 2007 🏛 John Wiley and Sons 🌐 English ⚖ 202 KB

## Abstract In this paper, we first show that quite different from the autonomous case, the exact boundary controllability for non‐autonomous wave equations possesses various possibilities. Then we adopt a constructive method to establish the exact boundary controllability for one‐dimensional non‐a

Global exact boundary controllability fo

Global exact boundary controllability for 1-D quasilinear wave equations

✍ Ke Wang 📂 Article 📅 2010 🏛 John Wiley and Sons 🌐 English ⚖ 156 KB

## Communicated by A. Kunoth Based on the local exact boundary controllability for 1-D quasilinear wave equations, the global exact boundary controllability for 1-D quasilinear wave equations in a neighborbood of any connected set of constant equilibria is obtained by an extension method. Similar

Exact Internal Controllability for the S

Exact Internal Controllability for the Semilinear Heat Equation

✍ Weijiu Liu; Graham H Williams 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 225 KB

Using the Browder᎐Minty surjective theorem from the theory of monotone operators, we consider the exact internal controllability for the semilinear heat 2 Ž . equation. We show that the system is exactly controllable in L ⍀ if the nonlinearities are globally Lipschitz continuous. Furthermore, we pro

Exact controllability for the magnetohyd

Exact controllability for the magnetohydrodynamic equations

✍ Viorel Barbu; Teodor Havârneanu; Cătălin Popa; S. S. Sritharan 📂 Article 📅 2003 🏛 John Wiley and Sons 🌐 English ⚖ 390 KB

## Abstract We study the local exact controllability of the steady state solutions of the magnetohydrodynamic equations. The main result of the paper asserts that the steady state solutions of these equations are locally controllable if they are smooth enough. We reduce the local exact controllabil

Oscillatory asymptotic expansion for sem

Oscillatory asymptotic expansion for semilinear wave equation

✍ Stefania Di Pomponio 📂 Article 📅 2001 🏛 John Wiley and Sons 🌐 English ⚖ 144 KB

## Abstract We study oscillatory properties of the solution to semilinear wave equation, assuming oscillatory terms in initial data have sufficiently small amplitude. The main result gives an a priori estimate of the remainder in the approximation by means of the method of __geometric optics__. The

Exact boundary observability for 1-D qua

Exact boundary observability for 1-D quasilinear wave equations

✍ Tatsien Li (Daqian Li) 📂 Article 📅 2006 🏛 John Wiley and Sons 🌐 English ⚖ 91 KB

## Abstract By means of a direct and constructive method based on the theory of semi‐global __C__^2^ solution, the local exact boundary observability and an implicit duality between the exact boundary controllability and the exact boundary observability are shown for 1‐D quasilinear wave equations