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Recent Advances in Differential Equations and Applications.

By: García Guirao, Juan Luis.
Contributor(s): Murillo Hernández, José Alberto | Periago Esparza, Francisco.
Material type: TextTextSeries: eBooks on Demand.SEMA SIMAI Springer Ser: Publisher: Cham : Springer, 2019Copyright date: ©2019Description: 1 online resource (250 pages).Content type: text Media type: computer Carrier type: online resourceISBN: 9783030003418.Subject(s): Differential equationsGenre/Form: Electronic books.Additional physical formats: Print version:: Recent Advances in Differential Equations and ApplicationsDDC classification: 515.35 LOC classification: QA1-939Online resources: Click here to view this ebook.
Contents:
Intro -- Preface -- Contents -- Contributors -- About the Editors -- Applications of Observability Inequalities -- 1 Introduction -- 2 Observability Inequalities -- 3 Applications of Observability Inequalities -- 3.1 Minimal Time Control Problems -- 3.2 Minimal Norm Control Problems -- 4 Open Problems -- References -- Optimal Design of Piezoelectric Microactuators: Linear vs Non-linear Modeling -- 1 Introduction -- 2 Topology Optimization of Piezoelectric Microactuators -- 2.1 Robust Formulation -- 3 Numerical Implementation -- 4 Examples -- 4.1 Maximizing Displacement in Horizontal Direction -- 4.2 Maximizing Displacement in Horizontal Direction Including Void Passive Area -- 4.3 Maximizing Displacement in Vertical Direction Including Void Passive Area -- 5 Comparison Between Linear and Non-linear Modeling -- 6 Conclusions -- References -- Formulation and Analysis of a Class of Direct Implicit Integration Methods for Special Second-Order I.V.P.s in Predictor-Corrector Modes -- 1 Introduction -- 2 Formulations of Falkner Methods in P-C Mode -- 2.1 Explicit Methods -- 2.1.1 PP'E Mode -- 2.1.2 PEC' Mode -- 2.2 Implicit Methods -- 2.2.1 P'PECE Mode -- 2.2.2 PEC'CE Mode -- 2.2.3 PECEC' Mode -- 3 Error Analysis -- 3.1 Local Truncation Errors -- 3.2 Accumulated Truncation Errors -- 3.2.1 P'PECE Mode -- 3.2.2 PEC'CE Mode -- 3.2.3 PECEC' Mode -- 4 Stability -- 5 Numerical Examples -- 5.1 Example 1 -- 5.2 Example 2 -- 5.3 Example 3 -- 5.4 Example 4 -- 5.5 Example 5 -- 6 Conclusions -- References -- Application of a Local Discontinuous Galerkin Method to the 1D Compressible Reynolds Equation -- 1 Introduction -- 2 The Model Problem -- 3 Numerical Method -- 4 Numerical Examples -- 4.1 Test 1: Numerical Convergence -- 4.2 Test 2: p-Adaptivity -- 4.3 Test 3: A Rugous Surface Case -- 4.4 Test 4: A Head-Tape Recording System -- 5 Conclusions -- References.
Classical Symmetries for Two Special Cases of Unsteady Flow in Nanoporous Rock -- 1 Introduction -- 2 The Lie Method -- 2.1 Lie Point Symmetries -- 2.2 Lie Contact Symmetries -- 3 Lie Group Classification -- 3.1 Case 1: Flow of Weakly Compressible Fluid -- 3.2 Case 2: Isothermic Gas Flow -- 4 Conclusions -- References -- Asymptotic Behaviour of Finite Length Solutions in a Thermosyphon Viscoelastic Model -- 1 Introduction -- 2 Previous Results About Well Posedness and Global Attractor -- 3 Asymptotic Behaviour of Finite Length Solutions -- 3.1 Previous Results and Notations -- 3.2 Asymptotic Behaviour -- 3.3 Concluding Remarks -- 4 Numerical Experiments -- 4.1 Introduction -- 4.2 Numerical Conclusions -- References -- Conservation Laws and Potential Symmetries for a Generalized Gardner Equation -- 1 Introduction -- 2 Conservation Laws -- 3 First Level Potential Systems and Symmetries -- 4 Second-Level Potential Systems and Symmetries -- 5 Conclusions -- References -- On a Nonlocal Boussinesq System for Internal Wave Propagation -- 1 Introduction -- 2 Derivation of the Model -- 2.1 Euler System for Internal Waves -- 2.2 Non-dimensionalization -- 2.3 Boussinesq/Boussinesq Regime -- 3 Well-posedness -- 3.1 Linear well-posedness -- 3.2 Local Well-posedness of the Full Nonlinear System -- 4 Solitary Wave Solutions -- 4.1 Existence of Solitary Waves -- 5 Numerical Approximation to Solitary Waves -- 5.1 A Numerical Technique to Compute Solitary Wave Profiles -- 5.2 Numerical Results -- 6 Conclusions -- References -- Subdivision Schemes and Multiresolution Analyses: Focus on the Shifted Lagrange and Shifted PPH Schemes -- 1 Introduction -- 2 Subdivision Schemes and Associated Multiresolution Transform -- 2.1 Subdivision Schemes -- 2.1.1 General Construction -- 2.1.2 Shifted Lagrange and Shifted PPH Schemes -- 2.2 Multiresolution Transform.
3 Decimation Operators -- 3.1 The Linear Case -- 3.2 Extension to the Non-linear Perturbation Case -- 4 Prediction Errors and Details -- 4.1 Construction of the Details -- 4.2 Prediction Error Decay -- 5 Numerical Results -- 6 Conclusion -- References -- Modelling Sparse Saliency Maps on Manifolds: Numerical Results and Applications -- 1 Introduction -- 2 Superpixel Segmentation of the Image -- 3 Weighted Graph -- 4 Control Map -- 5 Non Local Operators -- 5.1 Non Local L0 for Saliency Detection -- 6 Non Local Total Variation Model -- 6.1 Numerical Resolution: Primal-Dual Algorithm -- 7 Saliency Map Segmentation -- 8 Numerical Results -- 9 Conclusions -- References -- Linear Elimination in Chemical Reaction Networks -- 1 Introduction -- 2 Chemical Reaction Networks -- 2.1 Elimination System -- 2.2 Some Further Concepts -- 3 Reactant-Noninteracting Species -- 3.1 The Interaction Graph -- 3.2 Ideas Underlying the Proof of Theorem 1 -- 4 Examples -- 4.1 Allosteric Kinase -- 4.2 Phosphorylation and Dephosphorylation -- References -- Minimal Set of Generators of Controllability Space for Singular Linear Systems -- 1 Introduction -- 2 Notations -- 3 Preliminaries -- 3.1 Quasi-Weierstraß Form -- 3.2 Controllability -- 4 Exact Controllability -- 5 Generators of Control Space -- 6 Conclusion -- References -- On Stability of Discontinuous Galerkin Approximations to Anisotropic Stokes Equations -- 1 Introduction -- 2 SIP DG Approximation of the Stokes Problem -- 2.1 SIP DG Discretization of Second Order Elliptic Equations -- 2.2 SIP DG Formulation of Stokes Equations -- 3 SIP DG Approximation of Anisotropic Stokes Equations -- 3.1 SIP DG Framework for Anisotropic Stokes Equations -- 3.2 Stability and Well-Posedness of the Discrete Scheme -- 4 Numerical Tests -- References -- Numerical Simulation of Wear-Related Problems in a Blast Furnace Runner.
1 Introduction -- 2 Physical Problem -- 3 Thermo-Hydrodynamic Problem -- 3.1 Free Surface Flow -- 3.2 Hydrodynamic Model -- 3.2.1 Initial Conditions -- 3.2.2 Boundary Conditions -- 3.3 Thermal Model -- 3.3.1 Radiation -- 3.3.2 Boundary Conditions -- 3.4 Results -- 4 Jet Impact Problem -- 4.1 Mathematical Model -- 4.1.1 Boundary Conditions -- 4.1.2 Initial Conditions -- 4.2 Results -- 5 Conclusion -- References.
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Electronic Book UT Tyler Online
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QA1-939 (Browse shelf) https://ebookcentral.proquest.com/lib/uttyler/detail.action?docID=5629333 Available EBC5629333

Intro -- Preface -- Contents -- Contributors -- About the Editors -- Applications of Observability Inequalities -- 1 Introduction -- 2 Observability Inequalities -- 3 Applications of Observability Inequalities -- 3.1 Minimal Time Control Problems -- 3.2 Minimal Norm Control Problems -- 4 Open Problems -- References -- Optimal Design of Piezoelectric Microactuators: Linear vs Non-linear Modeling -- 1 Introduction -- 2 Topology Optimization of Piezoelectric Microactuators -- 2.1 Robust Formulation -- 3 Numerical Implementation -- 4 Examples -- 4.1 Maximizing Displacement in Horizontal Direction -- 4.2 Maximizing Displacement in Horizontal Direction Including Void Passive Area -- 4.3 Maximizing Displacement in Vertical Direction Including Void Passive Area -- 5 Comparison Between Linear and Non-linear Modeling -- 6 Conclusions -- References -- Formulation and Analysis of a Class of Direct Implicit Integration Methods for Special Second-Order I.V.P.s in Predictor-Corrector Modes -- 1 Introduction -- 2 Formulations of Falkner Methods in P-C Mode -- 2.1 Explicit Methods -- 2.1.1 PP'E Mode -- 2.1.2 PEC' Mode -- 2.2 Implicit Methods -- 2.2.1 P'PECE Mode -- 2.2.2 PEC'CE Mode -- 2.2.3 PECEC' Mode -- 3 Error Analysis -- 3.1 Local Truncation Errors -- 3.2 Accumulated Truncation Errors -- 3.2.1 P'PECE Mode -- 3.2.2 PEC'CE Mode -- 3.2.3 PECEC' Mode -- 4 Stability -- 5 Numerical Examples -- 5.1 Example 1 -- 5.2 Example 2 -- 5.3 Example 3 -- 5.4 Example 4 -- 5.5 Example 5 -- 6 Conclusions -- References -- Application of a Local Discontinuous Galerkin Method to the 1D Compressible Reynolds Equation -- 1 Introduction -- 2 The Model Problem -- 3 Numerical Method -- 4 Numerical Examples -- 4.1 Test 1: Numerical Convergence -- 4.2 Test 2: p-Adaptivity -- 4.3 Test 3: A Rugous Surface Case -- 4.4 Test 4: A Head-Tape Recording System -- 5 Conclusions -- References.

Classical Symmetries for Two Special Cases of Unsteady Flow in Nanoporous Rock -- 1 Introduction -- 2 The Lie Method -- 2.1 Lie Point Symmetries -- 2.2 Lie Contact Symmetries -- 3 Lie Group Classification -- 3.1 Case 1: Flow of Weakly Compressible Fluid -- 3.2 Case 2: Isothermic Gas Flow -- 4 Conclusions -- References -- Asymptotic Behaviour of Finite Length Solutions in a Thermosyphon Viscoelastic Model -- 1 Introduction -- 2 Previous Results About Well Posedness and Global Attractor -- 3 Asymptotic Behaviour of Finite Length Solutions -- 3.1 Previous Results and Notations -- 3.2 Asymptotic Behaviour -- 3.3 Concluding Remarks -- 4 Numerical Experiments -- 4.1 Introduction -- 4.2 Numerical Conclusions -- References -- Conservation Laws and Potential Symmetries for a Generalized Gardner Equation -- 1 Introduction -- 2 Conservation Laws -- 3 First Level Potential Systems and Symmetries -- 4 Second-Level Potential Systems and Symmetries -- 5 Conclusions -- References -- On a Nonlocal Boussinesq System for Internal Wave Propagation -- 1 Introduction -- 2 Derivation of the Model -- 2.1 Euler System for Internal Waves -- 2.2 Non-dimensionalization -- 2.3 Boussinesq/Boussinesq Regime -- 3 Well-posedness -- 3.1 Linear well-posedness -- 3.2 Local Well-posedness of the Full Nonlinear System -- 4 Solitary Wave Solutions -- 4.1 Existence of Solitary Waves -- 5 Numerical Approximation to Solitary Waves -- 5.1 A Numerical Technique to Compute Solitary Wave Profiles -- 5.2 Numerical Results -- 6 Conclusions -- References -- Subdivision Schemes and Multiresolution Analyses: Focus on the Shifted Lagrange and Shifted PPH Schemes -- 1 Introduction -- 2 Subdivision Schemes and Associated Multiresolution Transform -- 2.1 Subdivision Schemes -- 2.1.1 General Construction -- 2.1.2 Shifted Lagrange and Shifted PPH Schemes -- 2.2 Multiresolution Transform.

3 Decimation Operators -- 3.1 The Linear Case -- 3.2 Extension to the Non-linear Perturbation Case -- 4 Prediction Errors and Details -- 4.1 Construction of the Details -- 4.2 Prediction Error Decay -- 5 Numerical Results -- 6 Conclusion -- References -- Modelling Sparse Saliency Maps on Manifolds: Numerical Results and Applications -- 1 Introduction -- 2 Superpixel Segmentation of the Image -- 3 Weighted Graph -- 4 Control Map -- 5 Non Local Operators -- 5.1 Non Local L0 for Saliency Detection -- 6 Non Local Total Variation Model -- 6.1 Numerical Resolution: Primal-Dual Algorithm -- 7 Saliency Map Segmentation -- 8 Numerical Results -- 9 Conclusions -- References -- Linear Elimination in Chemical Reaction Networks -- 1 Introduction -- 2 Chemical Reaction Networks -- 2.1 Elimination System -- 2.2 Some Further Concepts -- 3 Reactant-Noninteracting Species -- 3.1 The Interaction Graph -- 3.2 Ideas Underlying the Proof of Theorem 1 -- 4 Examples -- 4.1 Allosteric Kinase -- 4.2 Phosphorylation and Dephosphorylation -- References -- Minimal Set of Generators of Controllability Space for Singular Linear Systems -- 1 Introduction -- 2 Notations -- 3 Preliminaries -- 3.1 Quasi-Weierstraß Form -- 3.2 Controllability -- 4 Exact Controllability -- 5 Generators of Control Space -- 6 Conclusion -- References -- On Stability of Discontinuous Galerkin Approximations to Anisotropic Stokes Equations -- 1 Introduction -- 2 SIP DG Approximation of the Stokes Problem -- 2.1 SIP DG Discretization of Second Order Elliptic Equations -- 2.2 SIP DG Formulation of Stokes Equations -- 3 SIP DG Approximation of Anisotropic Stokes Equations -- 3.1 SIP DG Framework for Anisotropic Stokes Equations -- 3.2 Stability and Well-Posedness of the Discrete Scheme -- 4 Numerical Tests -- References -- Numerical Simulation of Wear-Related Problems in a Blast Furnace Runner.

1 Introduction -- 2 Physical Problem -- 3 Thermo-Hydrodynamic Problem -- 3.1 Free Surface Flow -- 3.2 Hydrodynamic Model -- 3.2.1 Initial Conditions -- 3.2.2 Boundary Conditions -- 3.3 Thermal Model -- 3.3.1 Radiation -- 3.3.2 Boundary Conditions -- 3.4 Results -- 4 Jet Impact Problem -- 4.1 Mathematical Model -- 4.1.1 Boundary Conditions -- 4.1.2 Initial Conditions -- 4.2 Results -- 5 Conclusion -- References.

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