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Format: 1 online resource (250 pages)

Edition: 1st ed.

ISBN: 9783031622656

Series Statement: Trends in Mathematics Series

Note: Intro -- Preface -- Contents -- Part I Control of Partial Differential Equations -- Energy Decay Estimate for a Wave-Plate Interface Transmission Problem with Only Two Dynamical Boundary Controls -- 1 Introduction -- 2 Well-Posedness of the Problem -- 3 Some Regularity Results -- 4 Strong Stability with Non-compact Resolvent -- 5 Polynomial Stability -- 6 Conclusion and Open Problems -- References -- Uniform Stabilization of an Acoustic System -- 1 Introduction -- 2 Preliminaries and Main Results -- 3 Tools -- 3.1 Pseudo-Differential Tools -- Composition -- Commutator -- Adjoint -- Operators Bounded on L2 -- Gårding Inequality -- 3.2 Uniform Stabilization -- 4 Introduction of a Semiclassical Measure -- 4.1 Semiclassical Measure -- 4.2 The Measure Is Not Identically Null -- 4.3 The Semiclassical Measure Null on Support of Damping -- 5 Propagation of the Support -- 6 Some Properties on Semiclassical Measure -- 6.1 Properties of Measure -- References -- Observability and Control of Parabolic Equations on Networks -- 1 Introduction -- 1.1 Basic Definitions -- 1.2 Controllability Results -- 1.3 Application to the Resolution of Inverse Problems -- 2 The Observability Problem -- 2.1 Construction of the Auxiliary Function -- 2.2 A New Carleman Inequality -- References -- Some Results on the Energy Decay of Solutions for a Wave Equation with a General Internal Feedback of Diffusive Type -- 1 Introduction -- 2 Preliminaries Results -- 3 Global Existence -- 4 Lack of Exponential Stability -- 5 Asymptotic Stability -- 5.1 Strong Stability of the System -- 5.2 General Decay Estimate -- 5.3 Spectral Analysis -- 5.4 Optimality of Energy Decay in One-Dimensional Case -- 5.5 Polynomial Stability (for η=0) -- References -- Numerical Approximation of the Boundary Control for the Wave Equation with Periodic Oscillating Coefficients -- 1 Introduction. , 2 Characterization of the Control -- 3 Matrix Formulation of the Control Problem -- 4 Numerical Approximation of the Control Problem -- 5 Numerical Experiments -- References -- Numerical Impulse Controllability for Parabolic Equations by a Penalized HUM Approach -- 1 Introduction and Main Results -- 2 Preliminary Results -- 2.1 Dirichlet Case -- 2.2 Neumann Case -- 2.3 Dynamic Case -- 3 Algorithm for Calculating HUM Impulse Controls -- 3.1 The HUM Impulse Controls -- 3.2 Numerical Experiments -- 3.3 Dirichlet Case -- 3.4 Neumann Case -- 3.5 Dynamic Case -- References -- Part II Related Fields -- Decoding the Kramers-Fokker-Planck Operator: An Overview -- 1 Introduction -- 2 Analysis of the Kramers-Fokker-Planck Operator -- 2.1 Maximal Accretivity -- 2.2 Links with Witten Laplacians -- 3 Compactness Criteria for the Resolvent of Kramers-Fokker-Planck Operator -- 3.1 Initial Known Results -- 3.2 Case of Polynomial Potential -- Degree Less than 3 -- Degree Greater than 2 -- 3.3 Case of Homogeneous Potential -- 4 Conclusion and Perspectives -- References -- Exponential Decay of Solutions to Linear Evolution Equations with Time-Dependent Time Delay -- 1 Introduction -- 2 Well-Posedness -- 3 Exponential Stability -- 4 A Nonlinear Model -- 5 Examples -- 5.1 The Damped Wave Equation -- 5.2 A Damped Elasticity System -- References -- Study of the Numerical Method for an Inverse Problem of a Simplified Intestinal Crypt -- 1 The Simplified Intestinal Crypt Model -- 1.1 The Stem-Progenitor Interaction Model -- 2 Inverse Problem -- 2.1 The Problem of Identifying the Function ρdcs(z) -- 2.2 Example of ρdcs Shapes and δρdcs Directions -- 3 Numerical Approximation -- 3.1 BGK Schemes for the Direct Problem -- 3.2 Adjoint Scheme Associated with BGK Scheme -- 3.3 Discrete Inverse Problem -- 4 Numerical Examples -- 4.1 Inverse Problem Results. , Appendix: Derivative of the Flux for 5-Point Schemes -- Derivative of the Flux with Respect to ρsc and ρpc -- Derivative of the Flux with Respect to ρdcs -- Derivative of the Flux in Respect of the Maxwellian Distributions -- Derivative of the Deep Crypt Secretory with Respect to Its Parameters -- References -- Solving Ill-Posed Inverse Problems via the Born Approximation -- 1 Introduction -- 2 An Abstract Setting for the Born Approximation to Ill-Posed Inverse Problems -- 3 The Born Approximation in Inverse Spectral Theory -- 4 The Born Approximation for the Calderón Problem -- 5 Toward a General Born Approximation for the Calderón Problem -- References -- Central Nervous System Action on Rolling Balance Board Robust Stabilization: Computer Algebra and MID-Based Feedback Design -- 1 Introduction -- 2 Mechanical Model -- 3 Background and Prerequisites -- 3.1 Cauchy's Argument Principle -- 3.2 The Stepan-Hassard Approach -- 3.3 Background on Gröbner Bases -- 3.4 Cell Decomposition in CAD Routine -- 3.5 The MID Paradigm: A Partial Pole-Placement Strategy -- 3.6 Algorithmic Investigation of the MID Property -- 4 Main Results -- 4.1 A Normalized Fourth-Order Friction-Free Model -- 4.2 Forcing Multiplicity -- Real-Rooted Elimination-Produced Polynomial -- Fredholm Representation of the Normalized Characteristic Function -- Constancy Sign of the Integrand qυ,σ -- Effective Admissible Region -- 4.3 Dominancy Sufficient Conditions -- Frequency Bound -- Dominancy -- 5 Conclusion -- References -- Index.

Additional Edition: Print version: Ammari, Kaïs Advances in Partial Differential Equations and Control Cham : Springer Basel AG,c2024 ISBN 9783031622649

Language: English