Nonlinear Differential Equations and Applications

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 Plasma-Vacuum Interface: Higher Order Expansion.- Combined Numerical/Experimental Analysis for Intracranial Aneurysms in a Computational Hemodynamics Patient-Specific Framework.

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