**Editors: Martin Burger, Luis Caffarelli and Peter Markowich **

In the last decade partial differential equations (PDEs) have become fundamentally important in socioeconomics, as descriptive tools in the qualitative and quantitative sense. PDE modelling is rapidly replacing other more classical approaches, like cellular automata and microscopic agent-based descriptions. Very often PDE modeling of socioeconomic processes is based on principles carried over from the physical and chemical sciences. An example for this process is given by how kinetic modes for opinion dynamics, wealth distribution in human societies and flocking dynamics are derived. Other important classes of PDE models used in socioeconomics are mean field games (forward-backward coupled viscous Hamilton-Jacobi and transport equations), certain free boundary problems (e.g. for price formation in economic markets) and optimal transportation techniques. The main goal of this issue is to show that PDE modeling of socioeconomic processes not only leads to new and important insights in the applied sciences but also pushes the frontiers of analytical and numerical techniques for highly complex nonlinear PDEs.

## Read

This issue on Partial differential equation models in the socio-economic sciences is now available to read online, including the Introduction which is free to access.

**Don't have access?**

If you would like to recommend this journal to your Librarian please fill out this form or contact sales@royalsociety.org

## Buy

This issue is available to buy in print.

We offer discounts for bulk orders of the print version of this journal issue for educational use (£20 per copy for 10 or more). Please contact Jackie Knapp for more information.

## Also of interest

**Related issues**

- Complex patterns in wave functions – drums, graphs, and disorder
- Entropy and convexity for nonlinear partial differential equations
- Fractional calculus and its applications
- Decoherence

**Read more content from all our journals on:**

*Philosophical Transactions A *covers the whole of the physical sciences, please take a look at all of our previous issues

**Why not submit an article to one of our sister journals?**

*Proceedings A* publishes research and review articles across the entire range of the physical and mathematical sciences.

*Journal of the Royal Society Interface* publishes cross-disciplinary research at the interface between the physical and life sciences.

## New content

REGISTER for table of contents email alerts to see the latest content published in Royal Society journals

## Propose an issue

Find out more about guest editing a theme issue of *Philosophical Transactions A* from our Guest Editor information page.