Nonlinear Differential Equations and Applications

This proceedings volume gathers selected, carefully reviewed works presented at the Portugal-Italy Conference on Nonlinear Differential Equations and Applications (PICNDEA22), held on July 4-6, 2022, at the University of Évora, Portugal. The main focus of this work lies in non-linear problems originating in applications and their treatment with numerical analysis. The reader will also find new advances on topics such as ordinary and partial differential equations, numerical analysis, topological and variational methods, fluid mechanics, operator theory, stability, and more. The Portugal-Italy Conference on Nonlinear Differential Equations and Applications convenes Italian and Portuguese researchers in differential equations and their applications to amplify previous collaboration and to follow and discuss new topics in the area. Reflecting the increasing teamwork involving the two mathematical communities, the conference has been opened to researchers from all nationalities. While researchers in analysis and related fields are the primary readership of this volume, PhD students can rely on this book as a valuable source to keep pace with recent advances in differential equations and cutting-edge applications.

Focuses on non-linear problems and their treatment with numerical analysis Touches on theoretical and practical aspects of ODE, PDE, topological and variational methods, fluid mechanics, and more Offers valuable resources for researchers and PhD students seeking to keep pace with new advances in the field

Auteur
Hugo Beirao da Veiga, Docteur en Sciences Mathématiques (Paris-IV Sorbonne, 1971); full Professor of Mathematics at Italian Universities from 1976 (retired 2011, from Pisa Univ.); at Madison and Minneapolis Universities (two academic years); at Lisbon University; at the Accademia Nazionale dei Lincei (Rome), 1990-93. In addition to several invitations as main speaker at international conferences, has been personally invited by several research centers including Courant Institute of Mathematical Sciences (New-York); Ecole Normale Supérieure (Paris); Institute for Advanced Study (Princeton); Collège de France (Paris); Accademia Sinica--Chinese Accad. of Sciences (Beijing); Steklov Math. Institute--Russian Accad. of Sciences (S. Petersburg), etc. He does research mainly in Partial Differential Equations.
Feliz Manuel Barrão Minhós, full Professor of Mathematics at University of Évora, got the PhD in Mathematics from the University of Évora, has hone research in Differential Equatios (ODE), Nonlinear Functional Analysis, Variational and Topological Methos to Boundary Value Problems, and is the Coordinator of the Research Center in Mathematics and Applications since 2017.

Nicolas Van Goethem is professor at the Mathematics Department and researcher at CMAFcIO research center, Faculty of Science, Lisbon, Portugal. He graduated and obtained his PhD from Université catholique de Louvain, Belgium. He was invited to carry on research at various institutions, such as University of Pisa, University College of London, Ecole polytechnique de Palaiseau, and SISSA, Trieste. He works on mathematical analysis with applications to mechanics and material science, in particular on fracture and dislocation modeling, and elasto-plasticity.

Luís Sanchez Rodrigues, Professor of Mathematics at Faculdade de Ciências da Universidade de Lisboa (retired 2018), got his PhD in Mathematics from Universidade de Lisboa in 1981. He has done research in Differential Equations (ODEs) and Nonlinear Functional Analysis. He coordinated CMAF (2004-2015) and CMAFcIO (20015-2017).

Contenu
Preface.- Some Optimal Design Problems with Perimeter Penalisation.- On a Rotational Smagorinsky model for turbulent fluids: an overview of recent results in the steady and unsteady case.- On a forward and a backward stochastic Euler equation.- Keller-Segel System: A Survey on Radial Steady States.- The Kernel of The Strain Tensor for Solenoidal Vector Fields with Homogeneous Normal Trace.- Power Law Approximation Results for Optimal Design Problems.- Long-time behaviour for solutions of systems of PDEs modeling suspension bridges.- Positive Solutions for The Fractional P-Laplacian Via Mixed Topological and Variational Methods.- Some Remarks on The Virtual Element Method for The Linear Elasticity Problem in Mixed Form.- On the Existence and Stability of 2d Compressible Current-Vortex Sheets.- Navier-Stokes Equations with Regularized Directional Boundary Condition.- Local and Nonlocal Liquid Drop Models.- Mathematical Analysis of Turbulent Flows Through Permeable Media.- Quantitative Study of The Stabilization Parameter in The Virtual Element Method.- Geometric Optics for Surface Waves on The PlasmaVacuum Interface: Higher Order Expansion.- Combined Numerical/Experimental Analysis for Intracranial Aneurysms in a Computational Hemodynamics Patient-Specific Framework.