Preface 1. Introduction 2. Conservation laws and differential equations 3. Characteristics and Riemann problems for linear hyperbolic equations 4. Finite-volume methods 5. Introduction to the CLAWPACK software 6. High resolution methods 7. Boundary conditions and ghost cells 8. Convergence, accuracy, and stability 9. Variable-coefficient linear equations 10. Other approaches to high resolution 11. Nonlinear scalar conservation laws 12. Finite-volume methods for nonlinear scalar conservation laws 13. Nonlinear systems of conservation laws 14. Gas dynamics and the Euler equations 15. Finite-volume methods for nonlinear systems 16. Some nonclassical hyperbolic problems 17. Source terms and balance laws 18. Multidimensional hyperbolic problems 19. Multidimensional numerical methods 20. Multidimensional scalar equations 21. Multidimensional systems 22. Elastic waves 23. Finite-volume methods on quadrilateral grids Bibliography Index.

https://depts.washington.edu/clawpack/book2/sample.pdf

Finite Volume Methods for Hyperbolic Problems

1980 Preface * 1999 Preface * 1999 Acknowledgements * Introduction * 1 Circular Logic * 2 Phase Singularities (Screwy Results of Circular Logic) * 3 The Rules of the Ring * 4 Ring Populations * 5 Getting Off the Ring * 6 Attracting Cycles and Isochrons * 7 Measuring the Trajectories of a Circadian Clock * 8 Populations of Attractor Cycle Oscillators * 9 Excitable Kinetics and Excitable Media * 10 The Varieties of Phaseless Experience: In Which the Geometrical Orderliness of Rhythmic Organization Breaks Down in Diverse Ways * 11 The Firefly Machine 12 Energy Metabolism in Cells * 13 The Malonic Acid Reagent ('Sodium Geometrate') * 14 Electrical Rhythmicity and Excitability in Cell Membranes * 15 The Aggregation of Slime Mold Amoebae * 16 Numerical Organizing Centers * 17 Electrical Singular Filaments in the Heart Wall * 18 Pattern Formation in the Fungi * 19 Circadian Rhythms in General * 20 The Circadian Clocks of Insect Eclosion * 21 The Flower of Kalanchoe * 22 The Cell Mitotic Cycle * 23 The Female Cycle * References * Index of Names * Index of Subjects

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/596B270197FE27DE5FABB598B6210622/S0025557200150892a.pdf/div-class-title-span-class-italic-the-geometry-of-biological-time-span-by-a-t-winfree-pp-544-dm68-corrected-second-printing-1990-isbn-3-540-52528-9-springer-div.pdf

The geometry of biological time , by A. T. Winfree. Pp 544. DM68. Corrected Second Printing 1990. ISBN 3-540-52528-9 (Springer)

to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).

关于Semigroups of Linear Operators and Applications to Partial Differential Equations的两个注解

Synchronization in complex networks of phase oscillators: A survey

We study a model of vehicular traffic flow, represented by a coupled system formed by a scalar conservation law, describing the evolution of cars density, and an ODE, whose solution is the position of a moving bottleneck, i.e., a slower vehicle moving inside the cars' flow. A fractional step approach is used to approximate the coupled model, and convergence is proved by compactness arguments. Finally, the limit of such an approximating sequence is proved to solve the original PDE-ODE model.

/pdf/moving-bottlenecks-in-car-traffic-flow-a-pde-ode-coupled-1m8y5d7o45.pdf

Moving Bottlenecks in Car Traffic Flow: A PDE-ODE Coupled Model

Global well-posedness and relaxation limits of a model for radiating gas

We consider a Euler system with dynamics generated by a potential energy functional. We propose a form for the relative energy that exploits the variational structure and we derive a relative energy identity. When applied to specific energies, this yields relative energy identities for the Euler–Korteweg, the Euler–Poisson, the Quantum Hydrodynamics system, and low order approximations of the Euler–Korteweg system. For the Euler–Korteweg system we prove a stability theorem between a weak and a strong solution and an associated weak-strong uniqueness theorem. In the second part we focus on the Navier–Stokes–Korteweg system (NSK) with non-monotone pressure laws, and prove stability for the NSK system via a modified relative energy approach. We prove the continuous dependence of solutions on initial data and the convergence of solutions of a low order model to solutions of the NSK system. The last two results provide physically meaningful examples of how higher order regularization terms enable the use of the relative energy framework for models with energies which are not poly- or quasi-convex, compensated by higher-order gradients.

Relative Energy for the Korteweg Theory and Related Hamiltonian Flows in Gas Dynamics

In this paper we are concerned with the study of the relaxation limit of
the 3-$D$ hydrodynamic model for semiconductors. We prove the convergence of the
weak solutions to the Euler-Poisson system toward the solutions to the drift-diffusion
system, as the relaxation time tends to zero.

The relaxation to the drift-diffusion system for the 3-$D$ isentropic Euler-Poisson model for semiconductors

The aim of this paper is the study of the relaxation limit of the 3-D bipolar hydrodynamic model for semiconductors. We prove the convergence for the weak solutions to the bipolar Euler–Poisson system towards the solutions to the bipolar drifthyphen;diffusion system, as the relaxation time tends to zero.

Corrado Lattanzio

Papers

Moving Bottlenecks in Car Traffic Flow: A PDE-ODE Coupled Model

Global well-posedness and relaxation limits of a model for radiating gas

Relative Energy for the Korteweg Theory and Related Hamiltonian Flows in Gas Dynamics

The relaxation to the drift-diffusion system for the 3-$D$ isentropic Euler-Poisson model for semiconductors

On the 3-d bipolar isentropic euler–poisson model for semiconductors and the drift-diffusion limit