Research Topic · Peer-Reviewed

Partial Differential Equations

Partial differential equations (PDEs) are equations relating an unknown function of several independent variables to its partial derivatives, and they are the principal mathematical language for describing systems that vary continuously in space and time. They express conservation and balance laws and govern phenome…

Curated from this journal's research 📚 5 peer-reviewed articles cited Cited 7× across the literature 🔖 ISSN 2643-2811 🗓 Reviewed July 2026

Overview

Partial differential equations (PDEs) are equations relating an unknown function of several independent variables to its partial derivatives, and they are the principal mathematical language for describing systems that vary continuously in space and time. They express conservation and balance laws and govern phenomena such as diffusion, heat conduction, wave propagation, fluid flow, and electromagnetic and gravitational fields. PDEs are classified by order, linearity, and type, the canonical second-order forms being parabolic equations like the diffusion and heat equations, hyperbolic equations like the wave equation, and elliptic equations like Laplace's and Poisson's equations, each with characteristic behaviour and appropriate initial and boundary conditions. Reaction-diffusion and advection-diffusion systems extend these to coupled, often nonlinear, settings. In model-based research PDEs and related differential systems underpin the quantitative modelling of biological and epidemiological dynamics, including compartmental and spatial models of infection spread and intracellular processes, where they capture how concentrations and populations evolve under transport, growth, and interaction terms. Because closed-form solutions exist only in special cases, analysis combines analytical methods with numerical schemes such as finite difference, finite element, and spectral methods. Studying PDEs provides tools for prediction, parameter estimation, stability and sensitivity analysis, and the simulation of complex physical, biological, and engineered systems.

Research published in this journal

5 peer-reviewed articles, ranked by relevance. Each links to its DOI.

How this research is being cited

The 5 articles above have been cited 7 times in the scholarly literature. Citation data via OpenAlex and Crossref, updated Jun 2026.

A sample of recent works citing this journal's research on Partial Differential Equations, linking to each citing work.

Editorial oversight

Curated from peer-reviewed research published in Model Based Research (ISSN 2643-2811).

Journal editorial board
Yoshiaki Kikuchi · Japan Yung-Yao Chen · Taiwan Yang Chen · United States

This page summarises published research for orientation; it is not medical or professional advice.