Recent Advances in PDEs: Analysis, Numerics and Control

This book contains the main results of the talks given at the workshop Recent Advances in PDEs: Analysis, Numerics and Control, which took place in Sevilla (Spain) on January 25-27, 2017. The work comprises 12 contributions given by high-level researchers in the partial differential equation (PDE) area to celebrate the 60th anniversary of Enrique Fernández-Cara (University of Sevilla). The main topics covered here are: Control and inverse problems, Analysis of Fluid mechanics and Numerical Analysis. The work is devoted to researchers in these fields.

Covers three different areas in Applied Mathematics Presents contributions from researchers with a high impact at international level All contributions were accepted after a thorough peer review process

Autorentext

Anna Doubova is an Associate Professor in the Department of Differential Equations and Numerical Analysis (EDAN), Universidad de Sevilla, Spain. She holds a degree in Mechanics and Applied Mathematics from Lomonosov University (Moscow) and a PhD in Mathematics from the Universidad de Sevilla. Her research relates to analysis, control and inverse problems of PDEs with applications in physics, engineering, biology and other sciences. She publishes regularly in high-impact international journals.

Manuel González Burgos, BS, PhD, is Full Professor of Mathematical Analysis in the Department of Differential Equations and Numerical Analysis, Universidad de Sevilla, Spain. His fields of specialization include partial differential equations and control theory, with a particular focus on the controllability properties of scalar and non-scalar parabolic problems with controls exerted in a part of the domain or on a part of the boundary. He has published over 35 papers in peer-reviewed journals.

Francisco M. Guillén-González, BS, PhD, is Full Professor of Mathematical Analysis in the Department of Differential Equations and Numerical Analysis, Universidad de Sevilla, Spain. His research interests include the mathematical and numerical analysis of PDE systems applied to other sciences. In particular, he has studied PDEs related to incompressible fluid mechanics, phase transitions and biological processes. He is the author of more than 70 papers in peer-reviewed journals.

Mercedes Marín Beltrán is an Associate Professor of Mathematical Analysis in the Department of Computing and Numerical Analysis at the Universidad de Córdoba, Spain. She received her BS and her PhD from the Universidad de Sevilla. She is the author of a number of publications in international journals on the development and analysis of advanced numerical methods for partial differential equations with applications to fluid dynamics and tumor growth.

Inhalt

1 F. Ammar Khodja and C. Dupaix, Essential spectrum and null controllability of some parabolic equations.- 2 F. D. Araruna. F. O. Matias, M. L. Oliveira, and S. M. S. Souza, Well-posedness and asymptotic behavior for a nonlinear wave equation.- 3 M. Benítez, A. Bermúdez and P. Fontán, A second-order linear Newmark method for Lagrangian Navier-Stokes equations.- 4 D. Bresch, M. Colin, X. Lin, and P. Noble, Lubrication Theory and Viscous Shallow-Water Equations.- 5 E. Casas, The Influence of the Tikhonov Term in Optimal Control of Partial Differential Equations.- 6 R. Codina, On the design of algebraic fractional step methods for viscoelastic incompressible ows.- 7 V. Hernández-Santamaría and L. de Teresa, Some remarks on the hierarchic control for coupled parabolic PDEs.- 8 D. Nina Huaman, J. Límaco, and Miguel R. Nuñez Chávez, Local null controllability of the N-dimensional Ladyzhenskaya-Smagorinsky with N-1 scalar controls.- 9 A. Münch, Numerical estimations of the cost of boundary controls for the equation yt - yxx + Myx = 0 with respect to .- 10 F. J. Marín, J. Martínez-Frutos, and F. Periago, Control of Random PDEs: an Overview.- 11 A. Coronel, F. Guillén-González, F. Marques, and M. Rojas-Medar, The Dubovitskii and Milyutin formalism applied to an optimal control problem in a solidification model.- 12 U. Biccari, M. Warma, and E. Zuazua, Local regularity for fractional heat equations.