Recent Advances in Differential Equations and Applications

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.

• 1 Applications of Observability Inequalities.- 2 Optimal Design of Piezoelectric Microactuators: Linear vs Non-linear Modeling.- 3 Formulation and Analysis of a Class of Direct Implicit Integration Methods for Special Second-Order I.V.P.s in Predictor-Corrector Modes.- 4 Application of a Local Discontinuous Galerkin Method to the 1D Compressible Reynolds Equation.- 5 Classical Symmetries for Two Special Cases of Unsteady Flow in Nanoporous Rock.- 6 Asymptotic Behaviour of Finite Length Solutions in a Thermosyphon Viscoelastic Model.- 7 Conservation Laws and Potential Symmetries for a Generalized Gardner Equation.- 8 On a Nonlocal Boussinesq System for InternalWave Propagation.- 9 Subdivision Schemes and Multiresolution Analyses: Focus on the Shifted Lagrange and Shifted PPH Schemes.- 10 Modelling Sparse Saliency Maps on Manifolds: Numerical Results and Applications.- 11 M. Linear Elimination in Chemical Reaction Networks.- 12 Minimal Set of Generators of Controllability Space for Singular Linear Systems.- 13 On Stability of Discontinuous Galerkin Approximations to Anisotropic Stokes Equations.- 14 Numerical Simulation of Wear-Related Problems in a Blast Furnace Runner.

“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)