Nonlinear Analysis, Geometry and Applications: Proceedings of the First NLAGA-BIRS Symposium, Dakar, Senegal, June 24–28, 2019

Preface
Contents
Null Controllability of a Nonlinear Population Dynamics with Age Structuring and Spatial Diffusion
1 Introduction and Mains Results
2 Approximate Null Controllability of an Auxiliary System
2.1 Observability Inequality
2.2 Proof of the Observability Inequality
2.3 Proof of the Approximate Null Controllability of the Auxiliary System
3 Null Controllability of the Nonlinear System
4 Numerical Simulations
4.1 Discretization and Simulation of Uncontrolled System
4.2 Construction of the Control and Numerical Simulation
5 Conclusion
References
Null Controllability of a System of Degenerate Nonlinear Coupled Equations Derived from Population Dynamics
1 Introduction
2 Well-Posedness of the Problem of Population Dynamic
3 Null Controllability of an Intermediate System
3.1 Intermediate System
3.2 Carleman Inequalities
3.3 An Observability Inequality Result
3.4 Null Controllability of the Intermediate System
4 Proof of the Main Result
References
Optimal Mass Transport for Activities Location Problem
1 Introduction
2 The Optimal Mass Transport Problem
3 Continuous Optimal Transport Models of Lg
3.1 The Direct Method
3.2 Existence of Solution
4 Discrete Optimal Transport for ALP
4.1 Definition and Basic Properties
4.2 Discrete Gromov–Wasserstein Distance
4.3 Discrete Optimal Transport Formulation of Lg
5 Numerical Simulations
5.1 Setting up AMPL Model and Results
5.2 Simulation Illustration
6 Conclusion and Perspectives
References
Cut-off Phenomenon for Converging Processes in the Sense of α-Divergence Measures
1 Introduction
2 The α-Divergence Measures
3 The Main Results
3.1 Relations About Distances Between Joint Distributions and Distances Between Marginal Distributions in the Independent Case
3.2 Characterization of the Cut-off Phenomenon
4 Simulations Results
4.1 Influence of the Parameter α
4.2 Influence of the Convergence Rate ρ and the Ergodic Constant R
5 Conclusion
Appendix
References
Stochastic Optimization in Population Dynamics: The Case of Multi-site Fisheries
1 Introduction
2 Modeling
2.1 Single Site Case
2.2 3 Sites Case
2.3 L Sites Case
3 Stochastic Optimization
3.1 Position of the Problem
3.2 Dynamic Programming Principle
4 Stochastic Optimization and Numerical Simulations in the Case of Single Site
4.1 Stochastic Optimization
4.1.1 Position of the Problem
4.1.2 Dynamic Programming Principle
4.1.3 Existence and Uniqueness
4.2 Numerical Simulations
References
A Hurwitz Like Characterization of GUAS Planar Switched Systems
1 Introduction
2 Mathematical Preliminaries
2.1 Stability Notions
2.2 A Useful Real Algebraic Geometry Tool
3 Stability Behavior of a Switched Planar System
3.1 Statement of Our Main Result
3.2 Strict or Large Common Quadratic Lyapunov Function
3.2.1 Systems with a Strict Common Quadratic Lyapunov Function
3.2.2 Systems with a Large Common Quadratic Lyapunov Function
3.3 Global Uniform Asymptotic Stable Switched Systems
References
OPV Virus Evolution: Assessing the Risk of cVDPV Outbreak
1 Introduction
2 Model Framework
2.1 Model Formulation
3 Mathematical Analysis
3.1 Basic Properties
3.2 The Disease Free Equilibrium of Model System (2.5) and Its Stability
3.2.1 The Disease Free Equilibrium
3.3 Global Stability of the DFE
3.4 Uniform Persistence
3.5 Existence of the Endemic Equilibrium and Its Stability
4 Numerical Simulation
4.1 Sensitivity Analysis
4.2 Numerical Analysis
5 Conclusion
Appendix A
Appendix B
References
A Scalable Engineering Combination Therapies for Evolutionary Dynamic of Macrophages
1 Introduction
2 Mathematical Models
2.1 Stability Analysis of the System
2.1.1 Existence of the Equilibrium Points
2.1.2 Stability of Equilibrium Points
2.2 Mutations and Therapy
2.2.1 Model of Mutations
2.2.2 Numerical Analysis of the Mutation Model
2.2.3 Combination of Therapies
3 Optimal Control
3.1 Algorithm and Numerical Results
3.1.1 Initial Problem
3.1.2 A Suboptimal L1 Controller
3.1.3 Implementation and Results
3.1.4 Parameters for the Implementation in Matlab
3.1.5 Experimental Results
4 Conclusion and Perspectives
References
Exact Steady Solutions for a Fifteen Velocity Model of Gas
1 Introduction
2 Statement of the Problem
2.1 The Discrete Velocity Model
2.2 The Boundary Conditions
3 Positivity of the Microscopic Densities Nk
3.1 The First Proof
3.2 The Second Proof
4 Existence and Boundedness of the Solution
4.1 Existence of Solutions of (4.4)
5 Exact Solutions
5.1 Maxwellian Solutions
5.2 Non Maxwellian Solutions
6 Steady Flow in Box
7 Conclusion
Appendix
The Kinetic Equations of the Model
The Conservation Equations of the Model
References
Monotony and Comparison Principle in Non Autonomous Size Structured Models
1 Introduction
2 Main Results
2.1 Proof of Theorem 2.8: Monotony
2.2 Proof of Theorem 2.10 and Theorem 2.11: Comparison Principle
3 Application
References
A Boundary Value Problem of Sand Transport Equations: An Existence and Homogenization Results
1 Introduction and Results
2 Existence and Estimates, Proof of Theorem 1.1
3 Homogenization and Corrector Results
3.1 On Two-Scale Convergence
3.2 Homogenization Results
3.3 Corrector Results
References
The Role of the Mean Curvature in a Mixed Hardy-Sobolev Trace Inequality
1 Introduction and Main Result
2 Preliminaries
3 Comparing μs(Ω) and SN,s
4 Existence of Minimizer for μs(Ω)
5 Proof of the Main Result
References
Coupling Between Shape Gradient and Topological Derivative in 2D Incompressible Navier-Stokes Flows
1 Introduction
2 Shape Derivative
3 Topological Derivative
3.1 Proof of the Main Result
3.1.1 Variation of the Trilinear Form
3.1.2 Variation of the Bilinear Form
3.1.3 Variation of the Cost Function
4 The Proposed Numerical Method
4.1 Optimization Algorithm
4.2 Numerical Results
References
Shape Reconstruction in a Non-linear Problem
1 Introduction
2 Study of a Quasi-Linear Boundary Problem
2.1 Hopf's Transformation
2.2 Existence Result by Fixed Point Method
2.2.1 Schauder's Fixed Point Theorem
3 Study of the Shape Reconstruction Problem
3.1 Shape Optimization Under the Uniform Cone Property
3.2 Optimality Condition and Monotony Properties
3.2.1 Algorithm and Convergence Result
3.2.2 Initialization
References
The ∂-Problem for the Differential Forms with Boundary Value in Currents Sense Defined in a Contractible Completely Strictly Pseudoconvex Domain of a Complex Manifold
1 Introduction
2 Preliminaries
3 Solving the Equation du=f
4 Solving ∂ for the Differential Forms with Boundary Value in Currents Sense
5 Solving ∂ for the Differential Forms with Boundary Value in Currents Sense in M Where D Is a Contractible Completely Strictly Pseudoconvex Domain
References
Introduction to the Resolution of dd for the Supercurrents in the Non-Archimedean Frame
1 Introduction
2 Preliminaries
2.1 Spaces of Stein
3 Real Differential Forms on Berkovich's Space
4 Resolution of the Equation du=T and of d'd''
References
Minimal Graphs on Three-Dimensional Walker Manifolds
1 Introduction
2 Three Dimensional Walker Manifolds
3 Local Surfaces in Walker Three-Dimensional Manifolds
4 Miminal Graphs on Three Dimensional Walker Manifolds
References
Quantitative Result on the Deviation of a Real Algebraic Curve from Its Vertical Tangents
1 Introduction
2 Variation of the Separator of P(X,y)
2.1 Basic Definitions, Preliminary and Intermediate Results
2.2 Proof of Theorem 2.4
3 Deviation of the Curve from Its Vertical Tangents
3.1 Basic Definition, Preliminary and Intermediate Results
3.2 Proof of Theorem 3.3
References
Algebraic Points of Degree at Most 2 on the Affine Curvey11 = x2(x-1)2
1 Introduction
2 Auxiliary Results
References