Evolutionary dynamic equations : stabilizability, observability, and controllability / Akram Ben Aissa, Khaled Zennir.

Format:

Book

Author/Creator:

Ben Aissa, Akram, author.

Zennir, Khaled, author.

Language:

English

Subjects (All):

Differentiable dynamical systems.

Evolution equations.

Differential equations, Partial.

Nonlinear systems.

Physical Description:

1 online resource (viii, 200 pages)

Edition:

1st ed.

Place of Publication:

Berlin ; Boston : Walter de Gruyter GmbH, [2025]

Summary:

The book discusses the stability, observability, and controllability of nonlinear systems of PDEs (such as Wave, Heat, Euler-Bernoulli beam, Petrovsky, Kirchhoff, equations, and more).

Contents:

Intro

Preface

Contents

1 Introduction

1.1 Basic knowledge

1.1.1 Necessary contractions in the C0-semigroup approach

1.1.2 Useful inequalities

2 Qualitative properties for impulsive wave equation: controllability and observability

2.1 Classical solution for the first-order impulsive wave equation

2.2 Impulse controllability

2.3 Impulse observability inequality

3 Viscoelastic wave equation with dynamic boundary conditions

3.1 Well-posedness of the problem via Lumer-Phillips theorem

3.2 C0-semigroup approach and stability

4 Passage from internal exact controllability of beam equation to pointwise exact controllability

4.1 Estimation and regularity results near a point

4.2 Internal exact controllability of the beams equation

4.3 An inverse inequality

4.4 Estimates on the controls

4.5 The weak* convergence

5 Second-order evolution equations with/without delay

5.1 Relation between the decay rate of the energy for systems with/without delay

5.2 The exponentially and polynomial rate

5.3 Applications for models with interior damping

5.3.1 Wave equation

5.3.2 The multidimensional wave equation

5.3.2.1 The influence of internal damping

5.3.2.2 The impact of boundary damping

5.3.3 Weakly coupled and partially damped with boundary delay

5.3.4 Euler-Bernoulli beam

6 Euler-Bernoulli beam conveying fluid equation with nonconstant velocity and dynamical boundary conditions

6.1 Well-posedness via Lax-Milgram theorem

6.2 The influence of the density and velocity on stability

7 Stabilization of dissipative nonlinear evolution models

7.1 Nonlinear Petrovsky-wave system

7.1.1 Faedo-Galerkin approach

7.1.2 Stability via multiplier method

7.2 Nondegenerate Kirchhoff system coupled with heat conduction

7.2.1 Unique weak solution

7.2.2 Exponential stability.

7.3 Nondegenerate Kirchhoff equation with localized nonlinear damping

8 Nonlinear Petrovsky-type models

8.1 Delayed Petrovsky equation with a nonlinear strong damping

8.1.1 Global solvability in Sobolev spaces

8.1.2 Stability for the energy

8.2 Petrovsky equation with a nonlinear strong dissipation

8.2.1 Well-posedeness and regularity

8.2.2 Asymptotic behavior via Lyapunov functional

8.3 Examples

Bibliography

Index.

Notes:

Description based on publisher supplied metadata and other sources.

Part of the metadata in this record was created by AI, based on the text of the resource.

ISBN:

9783112214350

9783112214626

3-11-221435-8

OCLC:

1531947594