Nonlinear Analysis, Geometry and Applications: Proceedings of the Second NLAGA-BIRS Symposium, Cap Skirring, Senegal, January 25–30, 2022

Preface
Contents
Stability Analysis and Uniform Persistence of the Dynamics of Cytotoxic Cells with Crowley-Martin Functional Response
	1 Introduction
	2 Model of Cytotoxic Cells
	3 Dynamic Properties
		3.1 Existence and Determination of Equilibrium Points
		3.2 Uniform Persistence of the Disease
		3.3 Stability Analysis of Equilibrium Points
	4 Numerical Simulations
	5 Conclusion and Perspectives
	Appendix
	References
Null Controllability by Birth Control for a PopulationDynamics Model
	1 Introduction and Mains Results
	2 Proof of Theorem 1.1 (Step 1)
		2.1 Proof of the Proposition 2.2
		2.2 Proof of the Step 1 of the Theorem 1.1
	3 Proof of Theorem 1.1 (Step 2)
	4 Proof of the Theorem 1.1 (Step 3): Large Time Null Controllability
	5 Proof of the Theorem 1.2: Non Existence of Control
	6 Numerical Simulations
		6.1 Discretization of the Controlled System
		6.2 Simulations of the Controlled System and Comments
	7 Conclusion
	References
Aedes Vertical Transmission Logistic Growth Mathematical Model for Assessing Arboviruses Maintenance in Environment: A Positive Semigroup Approach
	1 Introduction
	2 Preliminaries Results of the Model
		2.1 Semilinear Cauchy Problem of the Model
		2.2  R0 Formula and Asymptotic Behavior of the Homogeneous Cauchy Problem
	3 Solution and Asymptotic Behaviors of the Model
	References
Global Dynamics of a Spore Producing Pathogens Epidemic System with Nonlocal Diffusion Process
	1 Introduction
	2 Main Results
		2.1 Existence, Dissipativity, and Compactness of the Semiflow
		2.2 Pathogen Invasion Process in Uninfected Environment and Threshold Dynamics
	3 Numerical Simulations and Discussion
		3.1 Description of the Model Numerical Simulation
		3.2 Discussion
	4 General Remarks
	5 Proof of Theorem 2.2
	6 Proof of Theorem 2.4
	7 Proof of Theorem 2.5
		7.1 Proof of Theorem 2.5(i)
		7.2 Technical Materials and Uniform Persistence
		7.3 Proof of Theorem 2.5(ii)
	Appendix A: Proof of Claim 7.4
	References
Stochastic Reaction Network Modeling and Optimal Control for Covid-19
	1 Introduction
	2 Modeling
	3 Optimal Control Problem
		3.1 Study of Stochastic Differential Equation
		3.2 Position of the Problem
		3.3 Dynamic Programming Principle
		3.4 Existence and Uniqueness of the HJB Equation
	4 Numerical Simulation
		4.1 Numerical Scheme
		4.2 Covid19 Case Study: SDE
		4.3 Covid19 Case Study: The Optimal Control Problem
	5 Discussion
	6 Conclusion
	References
Bayesian Selection of Adaptive Bandwidth in Non-homogeneous Poisson Process Kernel Estimators for the Intensity Function
	1 Introduction
	2 Bayesian Adaptive Bandwidth Selector
		2.1 Prior Choice for hij
		2.2 Choice for Prior Parameter
		2.3 Posterior Distribution and the Bayes Estimators
	3 Simulation
		3.1 Simulations Results
		3.2 An Application to Real Data
	4 Conclusion
	References
Nonnegative Matrix Factorization and Log-Determinant Divergences
	1 Introduction
	2 Nonnegative Matrix Factorization (NMF) and Multiplicative Algorithms
	3 Basic Alpha-Beta Logarithm Determinant Divergence
	4 Main Results
		4.1 The Alpha Beta Log-Det Divergence
		4.2 Special Cases of the AB Log-Det Divergences and Distances
		4.3 New Measures of AB-Log-Det Divergence
		4.4 Potentiality AB Log-Det Divergence
		4.5 Algorithms for NMF Based on the AB-Log-Det Divergence
			4.5.1 Algorithm Multiplicative Based on the AB-Log-Det Divergence
			4.5.2 Conditions for Monotonic Descent of AB-Log-Det Divergence
	5 Applications
		5.1 Efficient Similarity for Covariance Matrices via the NMF Jensen-Bregman Log-Det Divergence
			5.1.1 Derivation of Multiplicative Algorithms for NMF Based on the Jensen-Bregman-Log-Det Divergence and the DR
			5.1.2 Computational Advantages
		5.2 Alpha-Beta-Log Det Divergence Applied to Spatial Filtering
		5.3 Restoration of Musical Spectograms
	6 Conclusion
	References
Study of the Shallow Water Equations with Variable Bathymetry in a Channel with Flather Open Boundary Condition
	1 Introduction
	2 Model
		2.1 Description of the Model
		2.2 Model Equations
		2.3 Boundary Conditions
		2.4 Initial Conditions
	3 Mathematical Analysis of the Model
		3.1 Temporal Discretization of the Model
		3.2 Mixed Variational Formulation
		3.3 Mixed Finite Element Approximation of Velocity Field and Free Surface Elevation
			3.3.1 Discrete Mixed Formulation
			3.3.2 Study of the Discrete Solution
	4 Numerical Results
		4.1 Numerical Simulation
		4.2 Results
	5 Conclusion
	References
Almost Periodic Solution for Non Autonomous Non Densely Defined Cauchy Problems
	1 Introduction
	2 Preliminaries
	3 Existence of Almost Periodic Solution
		3.1 Almost Periodic Functions
		3.2 Almost Periodic Solutions of the Inhomgeneous Problem
		3.3 Almost Periodic Solutions of the Semilinear Problem
	4 Example
	References
Homogenization of a Parabolic Equation with Random Coefficients: An Application to Sand Transport Equations
	1 Introduction
		1.1 Results
		1.2 On the Stochastically Two Scale Convergence in the Mean
	2 Existence and Estimates, Proof of Theorem 1.1
	3 Stochastically Two-Scale Mean Convergence
	References
Uniqueness and Stability in an Inverse Problem for Electromagnetic Forming of a Metal Jet
	1 Introduction
	2 Study of the Shape Optimization Problem
		2.1 Auxiliary Results
		2.2 Position of the Problem
		2.3 Existence of Solution of Shape Optimization Problem
	3 Optimality Condition of the Problem
		3.1 Preliminaries
		3.2 Derivation with Respect to the Domain
		3.3 Results of the Optimality Condition
	4 Uniqueness and Stability of the Solution
		4.1 Stability on the Border of the Solution
		4.2 Stability of the Solution
		4.3 Uniqueness of the Solution
	5 Identification of the Optimal Shape
	6 Conclusion and Perspectives
	References
Numerical and Theoretical Analysis for Optimal ShapeInverse Problems
	1 Introduction
	2 Shape Derivative Using the Lagrangian and Minimax Methods
		2.1 Shape Derivative
	3 Numerical Method Based on Polynomial Deformation
		3.1 Numerical Illustrations by Translation
			3.1.1 Description of the Proposed Algorithm
			3.1.2 Numerical Illustrations
		3.2 Numerical Illustrations by Parabolic Deformation
			3.2.1 Description of the Proposed Algorithm
			3.2.2 Numerical Illustrations
	4 Numerical Method by a General Geometric Deformation with a Shape Optimisation Problem
		4.1 Shape Derivative Using the Vector Field Method
		4.2 The Augmented Lagrangian Algorithm for Equality-Constrained Problems
		4.3 Regularization of the Shape Gradient
		4.4 Some Illustrations: Initial Domains
		4.5 Description of the Proposed Algorithm
		4.6  Numerical Illustrations
	References
Algorithms for Nonlinear Integral Equations of Hammerstein Type with Phi-monotone Mappings in Certain Banach Spaces
	1 Introduction
	2 Preliminaries
	3 Convergence in lp, Lp and Wm,p-spaces, 1