Hyperbolic Conservation Laws (HCL)
- Introduction, models and their motivations (Traffic/Crowd Flow; Population Balance Eqs.; Image Processing)
- Linear and non-linear advection, diffusion or dispersion
- Characteristics, shocks, entropy and capillary-viscosity solution(s)
- Simplification/approximation by hyperbolic PDE models: capillary-viscosity limits
- A glance of numerical methods (front tracking; level set method; difference and finite volume methods)
Coagulation-Fragmentation Models (CFM)
- Overview of coagulation-fragmentation models
- Discrete models, existence and uniqueness results
- Mass conservation and gelation
- Continuous models with non- and singular rates
- Weak solutions, existence and uniqueness results
- Sectional methods to solve coagulation models
Continuous Modelling of Lithium Batteries (CMLB)
- Mass action law
- Basics of electrochemistry
- Transport of particles, electromigration, diffusion
Analysis and Numerics for Partial Differential Equations:
- Weak solutions, controllability stability and stabilizability for PDEs of evolution type
- Finite element method in blood flow, Finite volume method in population balance equations
- Convergence and error analysis of finite volume and element methods