Existence of generalized solutions of pde

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A Systematic Stability Analysis of Explicit Runge–Kutta Discontinuous Galerkin Methods for Maxwell'S Equations

Numerical Methods for Partial Differential Equations, Volume 41, Issue 5, September 2025.
ABSTRACT In this article, we carry out a systematic stability analysis for the explicit Runge–Kutta scheme coupled with a discontinuous Galerkin discretization in space for solving the time‐dependent Maxwell's equations. Many so‐called RKDG methods have been developed and successfully solved Maxwell's equations.
Yunqing Huang, Jichun Li, Haoke Zhao
wiley +1 more source

C ∞ regularity in semilinear free boundary problems. [PDF]

Math Ann
Restrepo D, Ros-Oton X.
europepmc +1 more source

Space‐Time Causal Discovery in Earth System Science: A Local Stencil Learning Approach

Journal of Geophysical Research: Machine Learning and Computation, Volume 2, Issue 3, September 2025.
Abstract Causal discovery tools enable scientists to infer meaningful relationships from observational data, spurring advances in fields as diverse as biology, economics, and climate science. Despite these successes, the application of causal discovery to space‐time systems remains immensely challenging due to the high‐dimensional nature of the data ...
J. Jake Nichol +5 more
wiley +1 more source

Nonlinear SPDEs and Maximal Regularity: An Extended Survey. [PDF]

Nonlinear Differ Equ Appl
Agresti A, Veraar M.
europepmc +1 more source

Embracing Uncertainty in “Small Data” Problems: Estimating Earthquakes From Historical Anecdotes

Journal of Geophysical Research: Machine Learning and Computation, Volume 2, Issue 3, September 2025.
Abstract Seismic risk estimates are greatly improved with an increased understanding of historical (and pre‐historical) seismic events. Although Bayesian inference has been shown to provide reasonable estimates of the location and magnitude of historical earthquakes from anecdotal tsunamigenic evidence, the validity and robustness of such an approach ...
N. E. Glatt‐Holtz +6 more
wiley +1 more source

Investigating fractal fractional PDEs, electric circuits, and integral inclusions via (ψ,ϕ)-rational type contractions. [PDF]

Sci Rep
Aldwoah K +5 more
europepmc +1 more source

Physics‐Informed Neural Networks for Solving the Two‐Dimensional Shallow Water Equations With Terrain Topography and Rainfall Source Terms

Water Resources Research, Volume 61, Issue 9, September 2025.
Abstract Solving the two‐dimensional Shallow Water Equations (SWE) is a fundamental problem in flood simulation technology. In recent years, physics‐informed neural networks (PINNs) have emerged as a novel methodology for addressing this problem. Given their advantages in parallel computing, potential for data assimilation and parameter calibration ...
Yongfu Tian +4 more
wiley +1 more source

Optimal approximations for the free boundary problems of the space-time fractional Black-Scholes equations using a combined physics-informed neural network. [PDF]

Sci Rep
Song L, Tan Y, Yu F, Luo Y, Zheng J.
europepmc +1 more source

Scientific Machine Learning of Flow Resistance Using Universal Shallow Water Equations With Differentiable Programming

Water Resources Research, Volume 61, Issue 9, September 2025.
Abstract Shallow water equations (SWEs) are the backbone of most hydrodynamics models for flood prediction, river engineering, and many other water resources applications. The estimation of flow resistance, that is, the Manning's roughness coefficient n $n$, is crucial for ensuring model accuracy, and has been previously determined using empirical ...
Xiaofeng Liu, Yalan Song
wiley +1 more source

A novel method for approximate solution of two point non local fractional order coupled boundary value problems. [PDF]

PLoS One
Tadoummant L +4 more
europepmc +1 more source

mathematics