Recent advances in differential equations and applications. ([2019])

• Record Type: Book
• Further Information: Note: Editors, Juan Luis García Guirao, José Alberto Murillo Hernández and Francisco Periago Esparza.
• Editors: García Guirao, Juan Luis; Murillo Hernández, José Alberto; Periago Esparza, Francisco
• 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 Area4.3 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 Errors3.2 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 Rock1 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 Remarks4 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
• Publisher Details: Cham, Switzerland : Springer
• Publication Date: 2019
• Extent: 1 online resource
• Subjects: 515.35; Differential equations; MATHEMATICS / Calculus; MATHEMATICS / Mathematical Analysis; Electronic books
• Languages: English
• ISBNs: 9783030003418; 3030003418
• Related ISBNs: 9783030003401; 303000340X
• Notes: Note: Includes bibliographical references.; Note: Online resource; title from PDF title page (EBSCO, viewed January 10, 2019).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
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