Recent Advances in Differential Equations and Applications

1. Front Matter

   Pages i-xiv

   PDF

2. Applications of Observability Inequalities

   • Jone Apraiz

   Pages 1-16

3. Optimal Design of Piezoelectric Microactuators: Linear vs Non-linear Modeling

   • David Ruiz, José Carlos Bellido, Alberto Donoso

   Pages 17-32

4. Formulation and Analysis of a Class of Direct Implicit Integration Methods for Special Second-Order I.V.P.s in Predictor-Corrector Modes

   • Higinio Ramos

   Pages 33-61

5. Application of a Local Discontinuous Galerkin Method to the 1D Compressible Reynolds Equation

   • Iñigo Arregui, J. Jesús Cendán, María González

   Pages 63-75

6. Classical Symmetries for Two Special Cases of Unsteady Flow in Nanoporous Rock

   • Tamara M. Garrido, Rafael de la Rosa, María Santos Bruzón

   Pages 77-86

7. Asymptotic Behaviour of Finite Length Solutions in a Thermosyphon Viscoelastic Model

   • Ángela Jiménez-Casas

   Pages 87-105

8. Conservation Laws and Potential Symmetries for a Generalized Gardner Equation

   • Rafael de la Rosa, Tamara M. Garrido, María Santos Bruzón

   Pages 107-119

9. On a Nonlocal Boussinesq System for Internal Wave Propagation

   • Angel Durán

   Pages 121-139

10. Subdivision Schemes and Multiresolution Analyses: Focus on the Shifted Lagrange and Shifted PPH Schemes

    • Zhiqing Kui, Jean Baccou, Jacques Liandrat

    Pages 141-155

11. Modelling Sparse Saliency Maps on Manifolds: Numerical Results and Applications

    • Euardo Alcaín, Ana Isabel Muñoz, Iván Ramírez, Emanuele Schiavi

    Pages 157-175

12. Linear Elimination in Chemical Reaction Networks

    • Meritxell Sáez, Elisenda Feliu, Carsten Wiuf

    Pages 177-193

13. Minimal Set of Generators of Controllability Space for Singular Linear Systems

    • María Isabel García-Planas

    Pages 195-210

14. On Stability of Discontinuous Galerkin Approximations to Anisotropic Stokes Equations

    • Francisco Guillén-González, María Victoria Redondo-Neble, José Rafael Rodríguez-Galván

    Pages 211-228

15. Numerical Simulation of Wear-Related Problems in a Blast Furnace Runner

    • Patricia Barral, Begoña Nicolás, Luis Javier Pérez-Pérez, Peregrina Quintela

    Pages 229-244

This work gathers a selection of outstanding papers presented at the 25^th Conference on Differential Equations and Applications / 15^th Conference on Applied Mathematics, held in Cartagena, Spain, in June 2017. It supports further research into both ordinary and partial differential equations, numerical analysis, dynamical systems, control and optimization, trending topics in numerical linear algebra, and the applications of mathematics to industry. The book includes 14 peer-reviewed contributions and mainly addresses researchers interested in the applications of mathematics, especially in science and engineering. It will also greatly benefit PhD students in applied mathematics, engineering and physics.

• Numerical methods for partial differential equations
• Optimal design
• Industrial mathematics
• Control theory
• Analysis of differential equations
• ordinary differential equations
• partial differential equations

“This is a book clearly aimed at experts, and most of the papers are focused on applications that are also very specialized.” (Bill Satzer, MAA Reviews, July 08, 2019)

• Department of Applied Mathematics and Statistics, Technical University of Cartagena, Cartagena, Spain

  Juan Luis García Guirao, José Alberto Murillo Hernández, Francisco Periago Esparza

Juan Luis García Guirao is a Full Professor of Applied Mathematics at the Technical University of Cartagena, Spain. He completed his Master’s and PhD in Mathematics at the Universidad de Murcia, Spain in 2001 and 2004. Under the supervision of Professor Francisco Balibrea, Full Professor of Mathematical Analysis and founder of the Dynamical Systems Group of the Region of Murcia he defended his Master’s Thesis in 2001 and PhD Thesis in 2004. His doctoral studies also involved a research stay at the Instituto Superior Tecnico in Lisbon under the supervision of Professor José Sousa-Ramos, one of the main researchers in Dynamical Systems in Portugal. He has held several positions at different universities, including the Universidad de Alicante, Universidad de Castilla-La Mancha, Universidad Autónoma de Barcelona, and Technical University of Cartagena. In 2011, at the age of 33, he became Spain’s youngest Full Professor of Mathematics. The author of more than 100 research paperspublished in prominent journals, he also serves on the Editorial Board of several journals, including MATCH Commun. Math. Comput. Chem., Open Physics, and Discrete Dynamics in Nature and Society. He has received a number of awards, e.g. the NSP 2017 for researchers younger than 40 years old, and the JDEA 2017 award for the best paper published in the field of Differential Equations. In addition, he has opened three research lines: discrete dynamical systems defined in low dimensional spaces, study of the periodic structure of smooth systems using the homological Lefschetz theory and analysis of Hamiltonian systems. Applications of the previous lines to problems from the fields of economics, chemistry and engineering are also considered.

José Alberto Murillo Hernández is an Associate Professor at the Department of Applied Mathematics and Statistics, Technical University of Cartagena, Spain. He received his Ph.D. in Mathematics from the University of Valencia, Spain and subsequently took part in a post-doctoral research stay at the Ecole Polytechnique in Paris, France supported by a grant from the European Union. His research interests include set-valued and nonsmooth analysis, viability theory and control. He is currently investigating the description and control of the evolution of sets driven by morphological equations.


Francisco Periago Esparza completed his PhD at the University of Valencia, Spain, in 1999. He is currently an Associate Professor at the Department of Applied Mathematics and Statistics and member of the Computational Mechanics and Scientific Computing group at the Technical University of Cartagena, Spain. His main research interests include optimal control, optimal design and controllability, both at the theoretical level and as applied to engineering problems. In the past few years, he has chiefly focused on optimal control for random PDEs.

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