The Net Advance of Physics

The Net Advance of Physics:
PARTIAL DIFFERENTIAL EQUATIONS

PARTIAL DIFFERENTIAL EQUATIONS:

General/Various:
- Analytical Methods in Physics by Yi-Zen Chu [2015] Textbook, 232 pp.
- The masterpieces of John Forbes Nash Jr by Camillo De Lellis [2016/06] 102 pp. "I have tried to rewrite four famous works of Nash [on partial differential equations] in a more modern language while adhering as much as possible to the original arguments."
- An Introduction to Partial Differential Equations by Per Kristen Jakobsen [2019/01] 225 pp.
- Introduction to Engineering Mathematics and Analysis: Modeling Physical Systems Using the Language of Mathematics by B. D. Wood [2023/05] Undergraduate textbook, 474 pp.
General: NUMERICAL METHODS: FINITE ELEMENT; MULTIGRID;
General: NUMERICAL METHODS: MACHINE LEARNING, etc.:
- An overview on deep-learning-based approximation methods for partial differential equations by C. Beck et al. [2020/12]
- Three ways to solve partial differential equations with neural networks by J. Blechschmidt and O. G. Ernst [2021/02]
- A hands-on introduction to Physics-Informed Neural Networks for solving partial differential equations with benchmark tests taken from astrophysics and plasma physics by H. Baty [2024/03]
Types: DIFFUSION; DIRAC; HEAT; KLEIN-GORDON; SCHROEDINGER; WAVE;
Type: AGGREGATION--DIFFUSION:
- Beginner's guide to aggregation--diffusion equations by D. Gómez-Castro [2023/09]
Type: CHOQUARD:
- A guide to the Choquard equation by Vitaly Moroz and Jean Van Schaftingen [2016/06]
Type: ELLIPTIC:
- An overview of periodic elliptic operators by Peter Kuchment [2015/10]
Type: FREE BOUNDARY:
- Obstacle problems and free boundaries: an overview by Xavier Ros-Oton [2017/07]
Type: KARDAR-PARISI-ZHANG and BURGER:
- The one-dimensional KPZ equation and its universality class by Jeremy Quastel and Herbert Spohn [2015/03]
- An appetizer to modern developments on the Kardar-Parisi-Zhang universality class by Kazumasa A. Takeuchi [Physica A 504, 77 (2018)]
Type: MULTISCALE: Re: WAVELETS: Goedecker and Ivanov 98/03;
Type: NONLINEAR:
- Symmetry and Integrability of Classical Field Equations by Costas J. Papachristou [2008/03]
- The one-dimensional KPZ equation and its universality class by Jeremy Quastel and Herbert Spohn [2015/03]
- An appetizer to modern developments on the Kardar-Parisi-Zhang universality class by Kazumasa A. Takeuchi [Physica A 504, 77 (2018)]
- Steady and Stable: Numerical Investigations of [error analysis of] Nonlinear Partial Differential Equations by R. Corban Harwood [2018/02]
Type: STOCHASTIC:
- Lectures on singular stochastic PDEs by M. Gubinelli and N. Perkowski [2014/08]
- A Gentle Introduction to Stochastic Partial Differential Equations: The Random Field Approach by Raluca M. Balan [2018/12]
- An Introduction to Singular Stochastic PDEs: Allen-Cahn Equations, Metastability and Regularity Structures by Nils Berglund [2019/01]
- Some Recent Progress in Singular Stochastic PDEs by Ivan Corwin and Hao Shen [2019/04]
- A concise introduction to control theory for stochastic partial differential equations by Q. Lü and X. Zhang [2021/01]
Type: TRICOMI:
- Tricomi Equation by Gui-Qiang Chen [2013/11]
Aspects: BÄCKLUND TRANSFORMATIONS:
- The Maxwell equations as a Bäcklund transformation by C. J. Papachristou [2015/05]
- Bäcklund Transformations: Some New and Old Perspectives by C. J. Papachristou and A. N. Magoulas [2016/07]
Aspects: EIGENFUNCTIONS:
- Park City lectures on Eigenfunctions [of the Laplacian] by Steve Zelditch [2013/10]
Aspects: INTEGRABILITY:
- Aspects of Integrability of Differential Systems and Fields by Costas J. Papachristou [2015/11]
Aspect: SPECTRAL THEORY:
- Spectral Theory of Partial Differential Equations - Lecture Notes by Richard S. Laugesen [2012/03] 120 pp.
Aspect: SYMMETRIES:
- The Differential Form Method for Finding Symmetries by B. Kent Harrison [2005/10]
- Symmetry and Integrability of Classical Field Equations by Costas J. Papachristou [2008/03]
Aspects: THIN-OBSTACLE PROBLEM:
- The thin-obstacle problem: A survey by X. Fernández-Real [2020/11]
Aspects: TWO-POINT FUNCTIONS:
- Two-point functions and their applications in geometry by S. Brendle [2014/02]
Aspects: VISCOSITY SOLUTIONS:
- Lecture notes on Viscosity Solutions for fully nonlinear 2nd order PDE and applications to Calculus of Variations in L^&inf; by Nikos Katzourakis [2014/11] 140 pp.
Re: CHAOS:
- Chaos in Partial Differential Equations, Navier-Stokes Equations and Turbulence by Y. Charles Li [2007/12]
- Chaos in Partial Differential Equations by Y. Charles Li [2009/09]
Re: GRAPHS:
- PDE Approaches to Graph Analysis by Justin Solomon [2015/05]
THE NET ADVANCE OF PHYSICS